Moving Charges and Magnetism · Question 1

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