Post Video Test - Moving charges and MagnetismContact Number: 9667591930 / 8527521718

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1.

Shown in the figure is a conductor carrying a current *I*. The magnetic field intensity at the point *O* (common centre of all the three arcs) is ($\theta $ in radian)

(1) $\frac{5{\mu}_{0}I\theta}{24\pi r}$ (2) $\frac{{\mu}_{0}I\theta}{24\mathrm{\pi r}}$

(3) $\frac{11{\mu}_{0}I\theta}{24\pi r}$ (4) zero

2.

Three long straight wires are connected parallel to each other across a battery of negligible internal resistance. The ratio of their resistances are 3 : 4 : 5. What is the ratio of distances of middle wire from the others if the net force experienced by it is zero

(1) 4 : 3 (2) 3 : 1 (3) 5 : 3 (4) 2 : 3

3.

A wire is bent to form a semi-circle of radius *a*. The wire rotates about its one end with angular velocity $\omega $. Axis of rotation being perpendicular to plane of the semicircle. In the space, a uniform magnetic field of induction B exists along the axis of rotation as shown. The correct statement is

(1) potential difference between P and Q is equal to 2*B*$\omega $*a*^{2}

(2) potential difference between P and Q is equal to 2$\pi $^{2}*B*$\omega $*a*^{2}

(3) *P* is at higher potential than *Q*

(4) potential difference between *P* and *Q* is zero.

4.

A conducting wire bent in the form of a parabola ${y}^{2}=2x$ carries a current *i* = 2A as shown in figure. This wire is placed in a uniform magnetic field $\overrightarrow{B}=-4\hat{k}$ tesla. The magnetic force on the wire is

(1) –16 $\hat{i}$ (2) 32 $\hat{i}$

(3) –32 $\hat{i}$ (4) 16 $\hat{i}$

5.

In the figure shown a coil of single turn is wound on a sphere of radius *R* and mass *m*. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. Current in the coil is *i*. The value of *B* if the sphere is in equilibrium is

(1) $\frac{mg\mathrm{cos}\theta}{\pi iR}$ (2) $\frac{mg}{\mathrm{\pi iR}}$

(3) $\frac{mg\mathrm{tan}\theta}{\pi iR}$ (4) $\frac{mg\mathrm{sin}\theta}{\pi iR}$

6.

Three infinitely long thin conductors are joined at the origin of coordinates and lies along the *x*, *y *and *z *axes. A current *i* flowing along the conductor lying along the negative *x*-axis divide equally into the other two at the origin. The magnitude of magnetic field at the point (0, –*a*, 0) is

(1) $\frac{{\mu}_{0}i}{4\pi a}$ (2) $\frac{3{\mu}_{0}i}{4\sqrt{2}\mathrm{\pi a}}$

(3) $\frac{\sqrt{5}{\mu}_{0}i}{8\pi a}$ (4) $\frac{\sqrt{3}{\mu}_{0}i}{2\pi a}$

7.

A uniform current carrying ring of mass *m* and radius *R* is connected by a massless string as shown. A uniform magnetic field ${B}_{0}$ exist in the region to keep the ring in horizontal position, then the current in the ring is (*l* = length of string)

(1) $\frac{mg}{{\mathrm{\pi RB}}_{0}}$ (2) $\frac{mg}{R{B}_{0}}$

(3) $\frac{mg}{3{\mathrm{\pi RB}}_{0}}$ (4) $\frac{mgl}{{\mathrm{\pi R}}^{2}{\mathrm{B}}_{0}}$

8.

A long wire having linear charge density $\lambda $ moving with constant velocity *v* along its length. A point charge moving with same speed in opposite direction and at that instant it is *r *distance from the wire. The net force acting on the charge is given by

(1) $\frac{\lambda q}{2\pi r}\left[\frac{1}{{\epsilon}_{0}}+{v}^{2}{\mu}_{0}\right]$ (2) $\frac{\lambda q}{2\pi r}\left[\frac{1}{{\epsilon}_{0}}-{\mu}_{0}{v}^{2}\right]$

(3) $\frac{\lambda q}{2\pi r}\sqrt{{\left(\frac{1}{{\epsilon}_{0}}\right)}^{2}+{v}^{4}{{\mu}_{0}}^{2}}$ (4) zero

9.

A cylindrical wire of radius R is carrying current i uniformly distributed over its cross-section. If a circular loop of radius r is taken as amperian loop, then the variation value of $\oint \overrightarrow{B}.\overrightarrow{dl}$ over this loop with radius 'r' of loop will be best represented by:

(1)

(2)

(3)

(4)

10.

Two infinitely long, thin, insulated, straight wires lies in the *x-y* plane along the *x* and *y*-axes respectively. Each wire carries a current *I*, respectively in the positive *x*-direction and positive *y*-direction. The magnetic field will be zero at all points on the straight line

(1) *y = x* (2) *y* = –*x*

(3) *y* = *x* – 1 (4) *y* = – *x* + 1

11.

There is a uniform magnetic field perpendicular to the plane of paper. A positive charged particle enters in the region, perpendicularly and collides inelastically at point *Q* to the rigid wall *MN*. If Co-efficient of restitution *e* = ½ then particle

(1) Retraces its path

(2) Strikes at point *O*

(3) Strikes at point *M*

(4) strikes at point *N*

12.

A circular current carrying loop of radius *R*, carries a current *i*. The magnetic field at a point on the axis of coil is $\frac{1}{\sqrt{8}}$ times the value of magnetic field at the centre. Distance of point from centre is

(1) $\frac{R}{\sqrt{2}}$ (2) $\frac{R}{\sqrt{3}}$ (3) $R\sqrt{2}$ (4) *R*

13.

The magnetic field at *O* due to current in the infinite wire forming a loop as shown in the following figure is

(1) $\frac{{\mu}_{0}I}{4\pi d}(\mathrm{cos}{\phi}_{1}+\mathrm{cos}{\phi}_{2})$

(2) $\frac{{\mu}_{0}}{4\pi}\times \frac{2I}{d}$

(3) $\frac{{\mu}_{0}I}{4\pi d}(\mathrm{sin}{\phi}_{1}+\mathrm{sin}{\phi}_{2})$

(4) $\frac{{\mu}_{0}}{4\pi}\times \frac{I}{d}$

14.

Two charged particles having charge *Q* and –*Q*, and masses *m* and 4*m* respectively enters in uniform magnetic field *B* at an angle $\theta $ with magnetic field from same point with speed *v*. The displacement from starting point where they will meet again, is

(1) $\frac{2\mathrm{\pi m}}{QB}v\mathrm{sin}\theta $ (2)$\frac{2\mathrm{\pi m}}{QB}v\mathrm{cos}\theta $

(3)$\frac{8\mathrm{\pi m}}{QB}v\mathrm{cos}\theta $ (4) $\frac{12\mathrm{\pi m}}{QB}v\mathrm{cos}\theta $

15.

A thin wire of length *l* is carrying a constant current. The wire is bent to form a circular coil. If radius of the coil, thus formed, is equal to *R* and number of turns in it is equal to *n*, then which of the following graphs represent(s) variation of magnetic field induction (B) at centre of the coil

(1)

(2)

(3)

(4) both 2 and 3

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