1

### JEE Main 2017 (Online) 8th April Morning Slot

A magnetic dipole in a constant magnetic field has :
A
maximum potential energy when the torque is maximum.
B
zero potential energy when the torque is minimum.
C
zero potential energy when the torque is maximum.
D
minimum potential energy when the torque is maximum.

## Explanation

In uniform magnetic field, the torque experienced by the magnetic dipole is $\tau$ = MB sin $\theta$

Torque will be maximum when $\theta$ = 90o

$\tau$max = MB sin90o = MB

Potential energy of magnetic dipole,

$\mu$ = $-$ MB cos $\theta$

at maximum torque,

$\mu$ = $-$ MB cos 90o = 0
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### JEE Main 2017 (Online) 8th April Morning Slot

Magnetic field in a plane electromagnetic wave is given by

$\overrightarrow B$ = B0 sin (k x + $\omega$t) $\widehat j\,T$

Expression for corresponding electric field will be :
Where c is speed of light.
A
$\overrightarrow E$ = B0 c sin (k x + $\omega$t) $\widehat k$ V/m
B
$\overrightarrow E$ = ${{{B_0}} \over c}$ sin (k x + $\omega$t) $\widehat k$ V/m
C
$\overrightarrow E$ = $-$ B0 c sin (kx +$\omega$t) $\widehat k$ V/m
D
$\overrightarrow E$ = B0 c sin (kx $-$$\omega t) \widehat k V/m ## Explanation The relation between electric and magnetic field is , C = {{\overrightarrow E } \over {\overrightarrow B }} \Rightarrow$$\,\,\,$ $\overrightarrow E$ = C $\overrightarrow B$

Electric field component is perpendicular to the direction of magnetic field. Given magnetic field is along y $-$ axis,

So, electric field along z $-$ axis will be

$\overrightarrow E$ = B0 C sin (kx + $\omega$t) $\,\widehat k$ v/m
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### JEE Main 2017 (Online) 9th April Morning Slot

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :
A
away from the wire
B
towards the wire
C
parallel to the wire along the current
D
parallel to the wire opposite to the current
4

### JEE Main 2017 (Online) 9th April Morning Slot

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the followingdifferent orientations which one corresponds to stable equilibrium ?
A
B
C
D