1
WB JEE 2022
+1
-0.25

An electron revolves around the nucleus in a circular path with angular momentum $$\overrightarrow L$$. A uniform magnetic field $$\overrightarrow B$$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $$\overrightarrow T$$, then

A
$$\overrightarrow T ||\overrightarrow L$$
B
$$\overrightarrow T$$ is anti-parallel to $$\overrightarrow L$$
C
$$\overrightarrow T \,.\,\overrightarrow L = 0$$
D
Angle between $$\overrightarrow T$$ and $$\overrightarrow L$$ is $$45^\circ$$
2
WB JEE 2022
+1
-0.25

A straight wire is placed in a magnetic field that varies with distance x from origin as $$\overrightarrow B = {B_0}\left( {2 - {x \over a}} \right)\widehat k$$. Ends of wire are at (a, 0) and (2a, 0) and it carries a current I. If force on wire is $$\overrightarrow F = I{B_0}\left( {{{ka} \over 2}} \right)\widehat j$$, then value of k is

A
1
B
5
C
$$-$$1
D
$${1 \over 2}$$
3
WB JEE 2022
+2
-0.5

A horizontal semi-circular wire of radius r is connected to a battery through two similar springs X and Y to an electric cell, which sends current I through it. A vertically downward uniform magnetic field B is applied on the wire, as shown in the figure. What is the force acting on each spring?

A
$$2\pi rBI$$
B
$${1 \over 2}\pi rBI$$
C
$$BIr$$
D
$$2BIr$$
4
WB JEE 2021
+1
-0.25

Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire passes through the point L at coordinates ($$-$$1, +1) and the other wire passes through the point M at coordinates ($$-$$1, $$-$$1). The resultant magnetic field at the origin O will be
A
$${{{\mu _0}I} \over {2\sqrt 2 \pi }}\widehat j$$
B
$${{{\mu _0}I} \over {2\pi }}\widehat j$$
C
$${{{\mu _0}I} \over {2\sqrt 2 \pi }}\widehat i$$
D
$${{{\mu _0}I} \over {4\pi }}\widehat i$$
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