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**Q.1. 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 : (2019)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.2. ****Ionized hydrogen atoms and Î±-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.3. ****A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 ÂµA and subjected to magnetic field of strength 0.85 T. Work done for rotating the coil by 180Âº against the torque is:- (2017)A: 4.55 ÂµJB: 2.3 ÂµJC: 1.15 ÂµJD: 9.1 ÂµJAns: **D

Solution:

W = MB (cosÎ¸

When it is rotated by angle 180Âº then

W = 2MB

W = 2 (NIA)B

= 2 x 250 x 85 x 10

= 9.1Î¼J

A:

B:

C:

D:

**Ans: **C

Solution:

**Q.5. 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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