CBSE Class 12 Physics Magnetic Effects Of Current Worksheet Set D

MAGNETIC EFFECT OF CURRENT & MAGNETISM

Question. Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 and 40 cm and they carry respectively 0.2 and 0.4 ampere current in opposite direction.
The magnetic field in weber/m² at the centre is
(a) μ₀/80
(b) 7μ₀/80
(c) (5/4) μ₀
(d) zero

Answer: D

Question. Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R₁ and R₂ respectively. The ratio of the mass of X to that of Y is
(a) √R₁/R₂
(b) (R₂/R₁)²
(c) (R₁/R₂)²
(d) √R₂/R₁

Answer: C

Question. Two straight long conductors AOB and COD are perpendicular to each other and carry currents I₁ and I₂. The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD is 

Answer: C

Question. Energy in a current carrying coil is stored in the form of
(a) electric field
(b) magnetic field
(c) dielectric strength
(d) heat

Answer: B

Question. A proton moving vertically downward enters a magnetic field pointing towards north. In which direction proton will deflect?
(a) East
(b) West
(c) North
(d) South

Answer: A

Question. The current sensitivity of a moving coil galvanometer depends on
(a) the number of turns in the coil
(b) moment of inertia of the coil
(c) current sent through galvanometer
(d) eddy current in Al frame

Answer: A

Question. An electron traveling with a speed u along the positive x-axis enters into a region of magnetic field where B = –B0 K̅ ( x > 0). It comes out of the region with speed v then
(a) v = u at y > 0
(b) v = u at y < 0
(c) v > u at y > 0
(d) v > u at y < 0

Answer: B

Question. When a charged particle moving with velocity v̅ is subjected to a magnetic field of induction B̅ , the force on it is nonzero. This implies that
(a) angle between v̅ and B̅ is necessarily 90°
(b) angle between v̅ and B̅ can have any value other than 90°
(c) angle between v̅ and B̅ can have any value other than zero and 180°
(d) angle between v̅ and B̅ is either zero or 180°

Answer: C

Question. Current i is flowing in a coil of area A & number of turns N, then magnetic moment of the coil is M is equal to
(a) NiA
(b) Ni/A
(c) Ni/√A
(d) N²Ai

Answer: A

Question. In cyclotron the charged particle may be accelerated upto energies
(a) Several eV
(b) MeV
(c) BeV
(d) Kev

Answer: B

Question. In cyclotron the resonance condition is
(a) the frequency of revolution of charged particle is equal to the frequency of A.C. voltage sources
(b) the frequency of revolution of charged particle is equal to the frequency of applied magnetic field
(c) the frequency of revolution of charged particle is equal to the frequency of rotation of earth
(d) the frequency of revolution of charged particle, frequency of A.C. source and frequency of magnetic field are equal

Answer: A

Question. Two parallel wires carrying currents in the same direction attract each other because of
(a) mutual inductance between them
(b) potential difference between them
(c) electric forces between them
(d) magnetic forces between them

Answer: D

Question. If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from the centre becomes approximately
(a) double
(b) three times
(c) four times
(d) one-fourth

Answer: C

Question. An infinitely long straight wire contains a uniformly continuous current of 10A. The radius of the wire is 4× 10^–2 m. The magnetic field at 2 × 10^–2 m from the centre of the wire will be:
(a) 0
(b) 2.5 × 10^–5 T
(c) 5.0 × 10^–5 T
(d) none of these.

Answer: B

Question. A proton and an a-particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25 m second to make 5 revolutions, then the time period for the a-particle would be
(a) 50 m sec
(b) 25 m sec
(c) 10 m sec
(d) 5 m sec

Answer: C

Question. To convert a galvanometer into an ammeter, one needs to connect a
(a) low resistance in parallel
(b) high resistance in parallel
(c) low resistance in series
(d) high resistance in series.

Answer: A

Question. A current carrying coil is subjected to a uniform magnetic field. The coil will orient so that its plane becomes
(a) inclined at 45° to the magnetic field
(b) inclined at any arbitrary angle to the magnetic field
(c) parallel to the magnetic field
(d) perpendicular to the magnetic field

Answer: D

Question. A charged particle moves through a magnetic field in a direction perpendicular to it. Then the
(a) velocity remains unchanged
(b) speed of the particle remains unchanged
(c) direction of the particle remains unchanged
(d) acceleration remains unchanged

Answer: B

Question. Protons and a-particles of equal momenta enter a uniform magnetic field normally. The radii of their orbits will have the ratio.
(a) 1
(b) 2
(c) 0.5
(d) 4

Answer: B

Question. A wire of length L metre carrying a current I ampere is bent in the form of a circle. Its magnitude of magnetic moment will be
(a) IL/4π
(b) I²L²/4π
(c) IL²/4π
(d) IL²/8π

Answer: C

Question. A solenoid of length 1.5 m and 4 cm diameter possesses 10 turns per cm. A current of 5A is flowing through it, the magnetic induction at axis inside the solenoid is (μ0 = 4π x 10^-7 weber amp^-1 m^-1)
(a) 4π x 10^-5 gauss
(b) 2π x 10^-5 gauss
(c) 4π x 10^-5 tesla
(d) 2π x 10^-5 tesla

Answer: D

Question. An electron (mass = 9 × 10^–31 kg, charge = 1.6 × 10^–19 C) moving with a velocity of 10⁶ m/s enters a magnetic field. If it describes a circle of radius 0.1m, then strength of magnetic field must be
(a) 4.5 × 10^–5 T
(b) 1.4 × 10^–5 T
(c) 5.5 × 10^–5 T
(d) 2.6 × 10^–5 T

Answer: C

Question. An electron moving with kinetic energy 6×10^–16 joules enters a field of magnetic induction 6 × 10^–3 weber/m² at right angle to its motion. The radius of its path is
(a) 3.42 cm
(b) 4.23 cm
(c) 5.17 cm
(d) 7.7 cm

Answer: A

Question. An electron moves in a circular arc of radius 10 m at a contant speed of 2 × 10⁷ ms^–1 with its plane of motion normal to a magnetic flux density of 10^–5 T. What will be the value of specific charge of the electron?
(a) 2 × 10⁴ C kg^–1
(b) 2 × 10⁵ C kg^–1
(c) 5 × 10⁶ C kg^–1
(d) 2 × 10¹¹ C kg^–1

Answer: D

Question. A current carrying loop in the form of a right angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, what is the force on the arm AC?
(a) -√2F̅
(b) -F̅
(c) F̅
(d) √2F̅

Answer: B

Question. If a current is passed through a spring then the spring will
(a) expand
(b) compress
(c) remains same
(d) None of these.

Answer: B

Question. A charged particle with velocity 2 × 10³ m/s passes undeflected through electric and magnetic field. Magnetic field is 1.5 tesla. The electric field intensity would be
(a) 2 × 10³ N/C
(b) 1.5 × 10³ N/C
(c) 3 × 10³ N/C
(d) 4/3 × 10^–3 N/C

Answer: C

Question. If in a circular coil A of radius R, current I is flowing and in another coil B of radius 2R a current 2I is flowing, then the ratio of the magnetic fields BA and BB, produced by them will be
(a) 1
(b) 2
(c) 1/2
(d) 4

Answer: A

Question. A circular loop of area 0.02 m² carrying a current of 10A, is held with its plane perpendicular to a magnetic field induction 0.2 T. The torque acting on the loop is
(a) 0.01 Nm
(b) 0.001 Nm
(c) zero
(d) 0.8 Nm

Answer: C

Question. The total charge induced in a conducting loop when it is moved in a magnetic field depends on
(a) the rate of change of magnetic flux
(b) initial magnetic flux only
(c) the total change in magnetic flux
(d) final magnetic flux only

Answer: C

Question. Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be
(a) 8 × 10^–7 N
(b) 8 × 10^–5 N
(c) 4 × 10^–7 N
(d) 4 × 10^–5 N

Answer: B

Question. A current of I ampere flows in a wire forming a circular arc of radius r metres subtending an angle q at the centre as shown.
The magnetic field at the centre O in tesla is

(a) μ₀Iθ/4πr
(b) μ₀Iθ/2πr
(c) μ₀Iθ/2r
(d) μ₀Iθ/4r

Answer: A

Question. A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with velocity pointed in the same direction. The electron will
(a) turn to its right
(b) turn to its left
(c) keep moving in the same direction but its speed will increase
(d) keep moving in the same direction but its speed will decrease

Answer: D

Question. A portion of a conductive wire is bent in the form of a semicircle of radius r as shown below in fig. At the centre of semicircle, the magnetic induction will be
(a) zero
(b) infinite
(c) μ₀/4π πi/r gauss
(d) μ₀/4π πi/rtesla

Answer: D

Question. A current of 3 A is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of 30º with the direction of the field. It experiences a force of magnitude
(a) 3 × 10^–4 N
(b) 3 × 10^–2 N
(c) 3 × 10² N
(d) 3 × 10⁴ N

Answer: B

Question. A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances a/2 and 2a respectively, from the axis of the wire is :
(a) 1/4
(b) 1/2
(c) 1
(d) 4

Answer: C

Question. The magnetic field at a distance r from a long wire carrying current i is 0.4 tesla. The magnetic field at a distance 2r is
(a) 0.2 tesla
(b) 0.8 tesla
(c) 0.1 tesla
(d) 1.6 tesla

Answer: A

Question. A cathode ray beam is bent in a circle of radius 2 cm by a magnetic induction 4.5 × 10^–3 weber/m². The velocity of electron is
(a) 3.43 × 10⁷ m/s
(b) 5.37 × 10⁷ m/s
(c) 1.23 × 10⁷ m/s
(d) 1.58 × 10⁷ m/s

Answer: D

Question. Two thin, long, parallel wires, separated by a distance ‘d’ carry a current of ‘i’ A in the same direction. They will
(a) repel each other with a force of μ₀i2/(2πd)
(b) attract each other with a force of μ₀i2/(2πd)
(c) repel each other with a force of μ₀i2/(2πd²)
(d) attract each other with a force of μ₀i2/(2πd²)

Answer: B

Question. A horizontal overhead powerline is at height of 4m from the ground and carries a current of 100A from east to west.
The magnetic field directly below it on the ground is (μ₀ = 4π × 10^–7 Tm A^–1)
(a) 2.5×10^–7 T southward
(b) 5 × 10^–6 T northward
(c) 5 × 10^–6 T southward
(d) 2.5 × 10^–7 T northward

Answer: C

Question. If an electron describes half a revolution in a circle of radius r in a magnetic field B, the energy acquired by it is
(a) zero
(b) 1/2 mv²
(c) 1/4 mv²
(d) pπ x Bev 

Answer: A

Question. A long solenoid carrying a current produces a magnetic field B along its axis. If the current is double and the number of turns per cm is halved, the new value of the magnetic field is
(a) 4 B
(b) B/2
(c) B
(d) 2 B

Answer: C

Question. A deutron of kinetic energy 50 keV is describing a circular orbit of radius 0.5m, in a plane perpendicular to magnetic field B̅ . The kinetic energy of a proton that discribes a circular orbit of radius 0.5m in the same plane with the same magnetic field B̅ is
(a) 200 keV
(b) 50 keV
(c) 100 keV
(d) 25 keV

Answer: C

Question. A cell is connected between two points of a uniformly thick circular conductor and i₁ and i₂ are the currents flowing in two parts of the circular conductor of radius a. The magnetic field at the centre of the loop will be
(a) zero
(b) μ₀/4π (I₁ - I₂)
(c) μ₀/2π (I₁ + I₂)
(d) μ₀/a (I₁ + I₂)

Answer: A

Question. In fig, what is the magnetic field induction at point O 

Answer: C

ONE MARK QUESTIONS

Question. State Biot Savart’s Law.
Answer: It states that magnetic field due to a small conductor of length dl, carrying a current I ,at a point at distance r, is given by, dB= μo/4∏. IdlsinӨ/r² where Ө is the angle between the direction of flow of current and the line joining the small conductor to the observation point.

Question. Write the dimensional formula of μ0.
Answer: The dimensional formula of μ0 is [M L T^-2A^-2]

Question. What is the effect of increasing the number of turns on magnetic field produced to a circular coil?
Answer: The magnetic field produced by a coil of n turns is n times the magnetic field produced by a coil of single turn.

Question. An electric charge enters in an electric field at right angles to the direction of electric field. What is the nature of the path followed? 
Answer: The electric charge will move along a parabolic path.

Question. An electron beam projected along +X- axis experiences a force due to a magnetic field along the +Y- axis. What is the direction of magnetic field?
Answer: The electron (a negatively charged particle) moving along + X- axis experiences force along +Y- axis, then the magnetic field must be directed along –Z- axis.

Question. Write an expression for the force experienced by a charged particle moving in a uniform magnetic field B.
Answer: The magnitude of force is given by Fm=B q v sin Θ

Question. Under which condition, an electron moving through a magnetic field experiences maximum force?
Answer: An electron moving through a magnetic field experiences maximum force, when it moves perpendicular to the direction of magnetic field .

Question. What is the work done by magnetic field on a moving charge and why?
Answer: Work done by magnetic field on a moving charge is zero. It is because, force on the charge due to magnetic field is perpendicular to its path.

Question. What is the nature of force, when the two parallel conductors carry currents in the (i) same direction (ii) opposite direction?
Answer: i) Force is attractive. ii) Force is repulsive.

Question. A circular coil of radius R carries a current I. Write the expression for the magnetic field due to this coil at centre.
Answer: B= μ0I/2R

Question. What is the angle of dip at the magnetic equator?
Answer: 0◦

Question. A jet plane is traveling west at 450m/s. If horizontal component of earths magnetic field at that place is 4X10^-4 T and angle of dip is 30^o, find emf induced between ends of wings having a span of 30m.
Answer: v = 450m/s, l = 30m, B = 4X10^-4T
e = Bvlsinө
= 4X10^-4 T X 450m/sX 30mXsin30^o
= 5.4Volt

Question. Give expression of magnetic field due to circular coil (at its centre) and due to long straight wire, when these are carrying current.
Answer: The magnetic field due to circular coil at its centre,
B=μo\4π. 2π n I a²/(a² + x²)^3/2
And magnetic field due to a long straight wire,
B=μo\4π .2I/a

Question. What is the nature of force, when the two parallel conductors carry currents in the (i) same direction (ii) opposite direction?
Answer: i) Force is attractive. ii) Force is repulsive.

Question. Give two factors by which the current sensitivity of a moving coil galvanometer can be increased.
Answer: Current sensitivity= n B A/k, Where the letters have their usual meanings.Since n and A cannot be increased beyond a limit, the current sensitivity may be increased by (i) by increasing B (ii) by decreasing k.

Question. Give two factors by which voltage sensitivity of a moving coil galvanometer can be increased.

Question. Using Biot Savart Law, derive an expression for the magnetic field at the centre of a circular coil of radius R, number of turns N, carrying current I.
Answer: Derivation.
Derive the expression using diagram.
B= μ0I/2R

Question. Using Ampere’s circuit Law, obtain an expression for the magnetic field along the axis of a current solenoid of length L carrying current I and having N number of turns.
Answer: Derivation.
Derive the expression using diagram.
B = μ0NI/L

Question. Desribe qualitatively, the path of a charged particle moving in a uniform electrostatic field with initial velocity (i)parallel to the field (ii) perpendicular to the field,(iii)at an arbitrary angle with the field direction.
Answer: (i) The force due to uniform electrostatic field will act along the direction of the field and hence path will be a straight line.
(ii) It will follow a parabolic path, as the force acts along a direction perpendicular to initial velocity.
(iii) It will follow parabolic path. The velocity of the charged particle may be resolved into two components.

Question. Write three magnetic elements of earth. Define them
Answer: Definition of angle of dip , angle of declination , Earths horizontal component

Question. Which of the following will describe the smaller circular path and when projected with same velocity perpendicular to magnetic field and why
Answer: r = mv/qB

Question. Give two factors by which voltage sensitivity of a moving coil galvanometer can be increased.
Answer: Voltage sensitivity= n B A/kR, Where the letters have their usual meanings. For higher voltage sensitivity; n B and A should be large, while k and R should be small. Since n and A cannot be increased beyond a limit, the voltage sensitivity may be increased by
(i) increasing B (ii) decreasing k and (iii) decreasing R.

Question. Steel is preferred for making permanent magnet whereas soft iron is preferred for making electromagnets. Give one reason.
Answer: High retentivity and high coercivity in case of steel. Low retentivity and low coercivity in case of soft iron.

Question. A uniform electric field and uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
(a) will turn towards right of direction of motion
(b) speed will decrease
(c) speed will increase
(d) will turn towards left direction of motion

Answer: B

Question. An electron enters a region where magnetic field (B) and electric field (E) are mutually perpendicular, then
(a) it will always move in the direction of B
(b) it will always move in the direction of E
(c) it always possesses circular motion
(d) it can go undeflected also

Answer: D

Question. An infinite straight conductor carrying current 2 I is split into a loop of radius r as shown in fig. The magnetic field at the centre of the coil is 

Answer: D

Question. A helium nucleus makes a full rotation in a circle of radius 0.8 meter in 2 sec. The value of the magnetic field induction B in tesla at the centre of circle will be
(a) 2 x 10^-19 μ₀
(b) 10^-19 μ₀
(c) 10^-19 μ₀
(d) 2 x 10^-20 μ₀

Answer: C

Question. A current of I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius r. The magnetic field at any point inside the cylinder at a distance x from the axis of the cylinder is
(a) ∞
(b) μ₀I/2πr
(c) μ₀I/2πx
(d) zero

Answer: D

Question. Two long parallel wires P and Q are held perpendicular to the plane of paper with distance of 5 m between them. If P and Q carry current of 2.5 amp. and 5 amp. respectively in the same direction, then the magnetic field at a point halfway between the wires is
(a) μ₀ /17
(b) 3 μ₀ / 2π
(c) μ₀ / 2π
(d) 3μ₀ / 2π

Answer: C

Question. A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field B̅0 such that B̅0 is perpendicular to the plane of the loop. The magnetic force acting on the loop is
(a) ir B₀
(b) 2π ir B₀
(c) zero
(d) π ir B0

Answer: C

Question. A square coil of side a carries a current I. The magnetic field at the centre of the coil is 

(a) μ₀I/aπ
(b) √2μ₀1/aπ
(c) μ₀1/√2aπ
(d) 2√2μ₀1/aπ

Answer: D

Question. The orbital speed of electron orbiting around a nucleus in a circular orbit of radius 50 pm is 2.2 × 106 ms–1. Then the magnetic dipole moment of an electron is
(a) 1.6 × 10^–19 Am²
(b) 5.3 × 10^–21 Am²
(c) 8.8 × 10^–24 Am²
(d) 8.8 × 10^–26 Am²

Answer: C

Question. A proton, deutron and an a-particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths?
(a) 1 : 2 : 2
(b) 2 : 1 : 1
(c) 1 : 1 : 2
(d) 1 : 2 : 1

Answer: A

Question. If an electron and a proton having same momenta enter perpendicular to a magnetic field, then
(a) curved path of electron and proton will be same (ignoring the sense of revolution)
(b) they will move undeflected
(c) curved path of electron is more curved than that of the proton
(d) path of proton is more curved

Answer: A

Question. A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 weber/m². The coil carries a current of 2A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be :
(a) 0.20 Nm
(b) 0.24 Nm
(c) 0.12 Nm
(d) 0.15 Nm

Answer: A

Question. The magnetic induction at a point P which is at a distance of 4 cm from a long current carrying wire is 10^–3 T. The field of induction at a distance 12 cm from the current will be
(a) 3.33 × 10^–4 T
(b) 1.11 × 10^–4 T
(c) 3 × 10^–3 T
(d) 9 × 10^–3 T

Answer: A

Question. Four wires, each of length 2.0 m, are bent into four loops P, Q, R and S and then suspended in a uniform magnetic field.
If the same current is passed in each, then the torque will be maximum on the loop 

(a) P
(b) Q
(c) R
(d) S

Answer: D

Question. A charged particle (charge q) is moving in a circle of radius R with uniform speed v. The associated magnetic moment μ is given by
(a) qvR²
(b) qvR²/2
(c) qvR
(d) qvR/2

Answer: D

Question. Tesla is the unit of
(a) magnetic flux
(b) magnetic field
(c) magnetic induction
(d)magnetic moment

Answer: B

Question. A straight wire of diameter 0.5 mm, carrying a current of 1A is replaced by another wire of 1mm diameter carrying the same current. The strength of magnetic field far away is
(a) unchanged
(b) quarter of its earlier value
(c) half of the earlier value
(d) twice the earlier value

Answer: A

Question. Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion
(a) depends on both R and v
(b) is independent of both R and v
(c) depends on R and not v
(d) depends on v and not on R

Answer: B

Question. A long wire is bent into shape ABCDE as shown in fig., with BCD being a semicircle with centre O and radius r metre. A current of I amp. flows through it in the direction A → B → C → D → E. Then the magnetic induction at the point O of the figure in vacuum is 

Answer: B

Question. A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be
(a) 2 : 1
(b) 1 : 4
(c) 4 : 1
(d) 1 : 2

Answer: B

Question. What is cyclotron frequency of an electron with an energy of 100 e V in the earth's magnetic field of 1 × 10^–4 weber / m2 if its velocity is perpendicular to magnetic field?
(a) 0.7 MHz
(b) 2.8 MHz
(c) 1.4 MHz
(d) 2.1 MHz

Answer: B

Question. A long solenoid has 1000 turns. When a current of 4A flows through it, the magnetic flux linked with each turn of the solenoid is 4 × 10^–3 Wb. The self inductance of the solenoid is : 
(a) 4H
(b) 3H
(c) 2H
(d) 1H

Answer: D

Question. A current loop in a magnetic field 
(a) can be in equilibrium in one orientation
(b) can be in equilibrium in two orientations, both the equilibrium states are unstable
(c) can be in equilibrium in two orientations, one stable while the other is unstable
(d) experiences a torque whether the field is uniform or non-uniform in all orientations

Answer: C

Question. A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is F̅ , the net force on the remaining three arms of the loop is
(a) 3F̅
(b) -F̅
(c) – 3F̅
(d) F̅

Answer: B

Question. A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 mA and subjected to magnetic field of strength 0.85 T. Work done for rotating the coil by 180º against the torque is
(a) 4.55 μJ
(b) 2.3 μJ
(c) 1.15 μJ
(d) 9.1 μJ

Answer: D