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**Q.1. A spherical conductor of radius 10 cm has a charge of 3.2 × 10 ^{-7} C distributed uniformly. what is the magnitude of electric field at a point 15 cm from the centre of the sphere? (2020)**

A: 6.28×10

B: 3.14×10

C: 6.28×10

D: 3.14×10

Ans:

Magnetic field for solenoid is given by

B = μ

n = N/ℓ

= 4π × 10

= 4 × 3.14 × 10

= 2000 × 3.14 × 10

= 6.14 × 10

A:

B:

C:

D:

**Ans: **C

Solution:

Inside (d < R) Magnetic field inside conductor

or B = Kd ...(i)

Straight line passing through origin

At surface (d = R)

...(ii)

Maximum at surface Outside (d > R)**Q.4. ****Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r _{H} : r_{a} will be : (2019)**A

A: 2 : 1

B: 1 : 2

C: 4 : 1

D: 1 : 4

Ans:

Solution:

**Q.5. ****A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 µA and subjected to magnetic field of strength 0.85 T. Work done for rotating the coil by 180º against the torque is:- (2017)A: 4.55 µJB: 2.3 µJC: 1.15 µJD: 9.1 µJAns: **D

Solution:

W = MB (cosθ

When it is rotated by angle 180º then

W = 2MB

W = 2 (NIA)B

= 2 x 250 x 85 x 10

= 9.1μJ

A:

B:

C:

D:

**Ans: **C

Solution:

**Q.7. 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 a radial distances a/2 and 2a respectively, from the axis of the wire is: (2016)A: 4B: 1/4C: 1/2D: 1Ans: **D

Solution:

Consider two amperian loops of radius a/2 and 2a as shown in the diagram.

Applying Ampere's circuital law for these loops, we get

B

Similarly, for bigger amperian loop,

Total current enclosed by amperian loop 2.

at a distance 2a from the axis of the wire.

A:

B:

C:

D:

Ans: B

Solution:

The point P is lying at a distance d along the z-axis.

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