Moving Charges and Magnetism

A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of 3.14 10-3 T at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively : (Take 0 = 4 10-7 T m/A)

1. 2.5 A, 20 A m2
2. 2 A, 4 A m2
3. 2.5 A, 2 A m2
4. 2 A, 10 A m2

The figure given below shows a long straight solid wire of circular cross-section of radius 'a' carrying steady current I. The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field (B) with distance (r) from the axis of the conductor in the region is : [figure]

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A galvanometer of resistance 100 Ω gives full scale deflection for a current of 1 mA. It is converted into an ammeter of range 0 – 10 A. The shunt required is :

1. 0.001 Ω
2. 0.10 Ω
3. 1.0 Ω
4. 0.01 Ω

A current I0 flows through a metallic circular loop of radius r as shown in the figure. Resistance of the segment ABC is half that of ADC. Magnitude of magnetic field at the centre O of the loop is : [figure]

1. 0 I02 r
2. 0 I012 r
3. 0 I04 r
4. 0 I02 r

Two infinitely long parallel conducting wires A and B carry currents I and 2I, respectively, in the same direction. The wire A has uniform mass per unit length and lies on an insulated floor. The wire B is kept fixed at a height h above the floor. The minimum magnitude of h so that the wire A does not rise from the floor is: [g is the acceleration due to gravity and 0 is the permeability of free space.]

1. 4 0 I2 g
2. 0 I22 g
3. 0 I2 g
4. 2 0 I2 g

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron)

1. heB m
2. heB2 m
3. he m
4. he2 m

An electron (mass 9 10-31 kg and charge 1.6 10-19 C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9 10-4 T perpendicular to its direction of motion. We wish to apply a uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 108 m s-1)

1. E is parallel to B and its magnitude is 27 102 V m-1
2. E is parallel to B and its magnitude is 27 104 V m-1
3. E is perpendicular to B and its magnitude is 27 104 V m-1
4. E is perpendicular to B and its magnitude is 27 102 V m-1

A 2 amp current is flowing through two different small circular copper coils having radii ratio 1 : 2. The ratio of their respective magnetic moments will be

1. 2 : 1
2. 4 : 1
3. 1 : 4
4. 1 : 2

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4 10-7 SI units):

1. 44 mT
2. 4.4 T
3. 4.4 mT
4. 44 T

A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field B = (2 i + 3 j - 4 k) T. The magnitude of the magnetic force acting on the wire is :

1. 5 IL
2. 5 IL
3. 3 IL
4. 3 IL

A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by : [figure]

1. 0 i4R pointed away from the page
2. 0 i4R [1 - 2 ] pointed away from page
3. 0 i4R [1 - 2 ] pointed into the page
4. 0 i4R pointed into the page

A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is

1. 6.28 10-2 T
2. 12.56 10-2 T
3. 12.56 10-4 T
4. 6.28 10-4 T

Given below are two statements: In light of above statements choose the most appropriate answer from the options given below.

1. Both Statement I and Statement II are correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct and Statement II is incorrect
4. Statement I is incorrect and Statement II is correct

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is

1. Uniform and remains constant for both the regions.
2. A linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.
3. A linearly increasing function of distance r upto the boundary of the wire and then decreasing one with 1r dependence for the outside region.
4. A linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one of the outside region.

A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by the wire of the coil is 1 A, the value of magnetic field produced at the centre of the coil will be (permeability of free space = 4 10-7 H/m) nearly

1. 10-3 T
2. 10-1 T
3. 10-2 T
4. 102 T

The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is

1. a plane
2. a straight line
3. circular
4. elliptical

Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is : ( 0 = 4 10-7 SI unit)

1. 1 10-4 N m-1 and is repulsive
2. 2 10-4 N m-1 and is attractive
3. 2 10-4 N m-1 and is repulsive
4. 1 10-4 N m-1 and is attractive

The magnetic field on the axis of a circular loop of radius 100 cm carrying current I = 2 A, at point 1 m away from the centre of the loop is given by :

1. 6.28 10-4 T
2. 3.14 10-7 T
3. 6.28 10-7 T
4. 3.14 10-4 T

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 105 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant. [figure]

1. 8 10-20 N
2. 4 10-20 N
3. 8 10-20 N
4. 4 10-20 N

In the product F = q ( v B ) = q v (B i + B j + B0 k ) For q = 1 and v = 2 i + 4 j + 6 k and F = 4 i - 20 j + 12 k What will be the complete expression for B?

1. 6 i + 6 j - 8 k
2. -8 i - 8 j - 6 k
3. -6 i - 6 j - 8 k
4. 8 i + 8 j - 6 k

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side 'a' (ii) A square of side 'a' The magnetic dipole moments of the coil in each case respectively are :

1. 4Ia2 and 3Ia2
2. 3 Ia2 and 3Ia2
3. 3Ia2 and Ia2
4. 3Ia2 and 4Ia2

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is : ( 0 = 4 10-7 T m A-1)

1. 3.14 10-4 T
2. 6.28 10-5 T
3. 3.14 10-5 T
4. 6.28 10-4 T

A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor, is correctly represented by the figure :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Ionized hydrogen atoms and α-particles with same momenta enter perpendicular to a constant magnetic field, B. The ratio of their radii of their paths rH : r will be :

1. 1 : 2
2. 4 : 1
3. 1 : 4
4. 2 : 1

A metallic rod of mass per unit length 0.5 kg m-1 is lying horizontally on a smooth inclined plane which makes an angle of 30 with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

1. 7.14 A
2. 5.98 A
3. 14.76 A
4. 11.32 A

Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is

1. 40
2. 25
3. 250
4. 500

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction as shown in figure. Magnitude of force per unit length on the middle wire 'B' is given by [figure]

1. 2 0 I2 d
2. 2 0 I2 d
3. 0 I2 2 d
4. 0 I22 d

A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180 against the torque is

1. 4.55
2. 2.3
3. 1.15
4. 9.1

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 distance a2 and 2a respectively, from the axis of the wire is

1. 1
2. 4
3. 14
4. 12