Moving Charges and Magnetism · Question 5

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