LEVEL – I

1. Two thin long parallel wires separated by a distance b are carrying a current i amp each. The magnitude of the force per unit length exerted by one wire on the other is:

(A) μ_{o}(i^{2}/b^{2})

(B)μ_{o}i^{2}/2πb

(C) μ_{o}i/2πb

(D) μ_{o}i/4πb

2. A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If a steady current I is established in the wire as shown in the figure, the loop will:

(A) rotate about an axis parallel to the wire

(B) move away from the wire

(C) move towards the wire

(D) remain stationary

3. The resulting magnetic field at the point O due to the current carrying wire shown in the figure:

(A) points out of the page

(B) points into the page

(C) is zero

(D) is the same as due to the segment WX along.

4. A particle enters the region of a uniform magnetic field as shown in figure. The path of the particle inside the field is shown by dark line.

The particle is:

(A) electrically neutral

(B) positively charged

(C) negatively charged

(D) information given is inadequate

5. In the given figure, what is the magnetic field induction at point O?

(A) $ \displaystyle \frac{\mu_0 I }{4 \pi r} $

(B) $ \displaystyle \frac{\mu_0 I}{4 r} + \frac{\mu_0 I}{2 \pi r} $

(C) $ \displaystyle \frac{\mu_0 I}{4 r} + \frac{\mu_0 I}{4 \pi r} $

(D) $ \displaystyle \frac{\mu_0 I}{4 r} – \frac{\mu_0 I}{4 \pi r} $

6. An electron is revolving around a proton in a circular orbit of diameter 1A°. If it produces a magnetic field of 14 wb/m^{2} at the proton, then its angular velocity will be about

(A) 8.75 × 10^{16} rad/s

(B) 10^{10} rad/s

(C) 4 × 10^{15} rad/s

(D) 10^{15} rad/s

7. Electrons at rest are accelerated by a potential of V volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field B. The radius of the path of the electrons inside the magnetic field is:

(A) $ \displaystyle \frac{1}{B} \sqrt{\frac{m V}{e}} $

(B) $ \displaystyle \frac{1}{B} \sqrt{\frac{2 m V}{e}} $

(C) $ \displaystyle \frac{V}{B} $

(D) $ \displaystyle \frac{1}{B} \sqrt{\frac{ V}{e}} $

8. Two long parallel wires carry currents i_{1} and i_{2} (i_{1} > i_{2}) when the currents are in opposite direction, the magnetic field at a point midway between the wires is 30 mT. If the direction of i_{2} is changed, the field becomes 10 mT . The ratio i_{1}/i_{2} is

(A) 1

(B) 3

(C) 2

(D) 4

9. An infinitely long straight conductor is bent into shape as shown in figure. It carries a current I A. and the radius of circular loop is r metre. Then the magnetic induction at the centre of the circular loop is:

(A) 0

(B) ∞

(C) $ \displaystyle \frac{\mu_0 i}{2 \pi r} (\pi + 1) $

(D) $ \displaystyle \frac{\mu_0 i}{2 \pi r} (\pi – 1) $

10. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

(A) straight line

(B) circle

(C) helix

(D) cycloid

### ANSWER:

1. (B) 2. (C) 3. (B) 4. (A) 5. (C) 6. (A) 7. (B) 8. (C) 9. (D) 10.(A)

LEVEL – I

11. A conductor of mass m and length l , carrying current i (direction as shown in the figure) is placed on smooth inclined making angle θ with horizontal. A magnetic field B is directed vertically upwards. Then for equilibrium of conductor tanθ is given by

(A) 2mg/Bil

(B) mg/Bil

(C) mg/2Bil

(D) Bil/mg

12. The magnetic field at centre of a hexagonal coil of side l carrying a current i is

(A) √3μ_{o}i/πl

(B) μ_{o} i/4πl

(C) πμ_{o}i/√3l

(D) zero

13. A conductor AB of length L carrying a current I_{1} is placed perpendicular to a long straight conductor x-y carrying a current I_{2}, as shown in the figure. The force on AB has magnitude is

(A) $ \displaystyle \frac{\mu_0 I_1 I_2 }{2 \pi } (log 2) $

(B) $ \displaystyle \frac{\mu_0 I_1 I_2 }{2 \pi } (log 3) $

(C) $ \displaystyle \frac{3 \mu_0 I_1 I_2 }{2 \pi } $

(D) $ \displaystyle \frac{2 \mu_0 I_1 I_2 }{3 \pi } $

14. A current i flows along a thin wire shaped as shown in figure. The radius of the curved part of the wire is r. The field at the centre O of the coil is :

(A) $ \displaystyle \frac{\mu_0 i }{4 r } $

(B) $ \displaystyle \frac{\mu_0 }{2 \pi r } $

(C) $ \displaystyle \frac{\mu_0 i }{2 \pi r } $

(D) $ \displaystyle \frac{\mu_0 i }{8 \pi r } (3 \pi + 4) $

15. A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x>b is

(A) qbB/m

(B) q(b-a)B/m

(C) qaB/m

(D) q(b+a)B/2m

16. A circular loop of mass m and radius r is kept in a horizontal position (X – Y plane) on a table as shown in figure. A uniform magnetic field B is applied parallel to x-axis. The current I in the loop, so that its one edge just lifts from the table, is:

(A) mg/πr^{2} B

(B) mg/πrB

(C) mg/2πrB

(D) πrB/mg

17. In figure there exists uniform magnetic field B into the plane of paper. Wire CD is in the shape of an arc and is fixed. OA and OB are the wires rotating with angular velocity ω as shown in figure in the same plane as that of the arc about point O. If at some instant OA = OB = l and each wire makes angle θ = 30° with y–axis, the current through resistance R is (wires OA and OB have no resistance)

(A) Zero

(B) Bωl^{2}/R

(C) Bωl^{2}/2R

(D) Bωl^{2}/4R

18. The wire loop shown in figure carries a current as shown. The magnetic field at the centre O is:

(A) zero

(B) $ \displaystyle \frac{\mu_0 i }{4 }(\frac{1}{R_1} – \frac{1}{R_2}) $

(C) $ \displaystyle \frac{\mu_0 i }{4 }(\frac{1}{R_1} + \frac{1}{R_2}) $

(D) $ \displaystyle \frac{\mu_0 i }{2 }(\frac{1}{R_1} – \frac{1}{R_2}) $

19. The magnetic field strength at a point P distant r due to an infinite straight wire as shown in the figure carrying a current i is:

(A) μ_{o}

(B)$ \displaystyle \frac{\mu_0 i }{2 \sqrt{2} r} $

(C) $ \displaystyle \frac{\mu_0 i }{\sqrt{2} \pi r} $

(D) $ \displaystyle \frac{\mu_0 i }{4 \pi r}(2 + \sqrt{2}) $

20. A wire bent in the form of a sector of radius r subtending an angle θ° at centre, as shown in figure is carrying a current i. The magnetic field at O is:

(A) $ \displaystyle \frac{\mu_0 i }{2 r} \theta $

(B) $ \displaystyle \frac{\mu_0 i }{2 r} (\theta /180 ) $

(C) $ \displaystyle \frac{\mu_0 i }{2 r} (\theta /360 ) $

(D) zero

##### ANSWER:

11. (D) 12. (A) 13. (B) 14. (D) 15. (C) 16. (B) 17. (B) 18. (B) 19. (D) 20. (C)