JEE Advanced PYQ Physics – Force and Torque on Current Carrying Conductor

Q 1 :

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_{0}$ , as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity $g$ , on two conducting supports at $P$ and $Q$ . When a current $I$ is passed through the loop, the loop turns about the line $P Q$ by an angle $θ$ given by [2024]

$\tan θ = \frac{π r I B_{0}}{m g}$
$\tan θ = \frac{2 π r I B_{0}}{m g}$
$\tan θ = \frac{π r I B_{0}}{2 m g}$
$\tan θ = \frac{m g}{π r I B_{0}}$

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(1)

Let the loop make an angle $θ$ with the vertical.

In equilibrium, $τ_{net} = 0$

$τ_{0} = M B \sin (90 - θ) - m g . r \sin θ = 0$

$I . π r^{2} . B_{0} \cos θ = m g r . \sin θ$

$∴$ $\frac{\sin θ}{\cos θ} = \frac{I π r^{2} B_{0}}{m g r}$

$∴$ $\tan θ = \frac{π r I B_{0}}{m g}$

Q 2 :

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to [2003]

contract
expand
move towards +ve $x$ -axis
move towards -ve $x$ -axis.

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(2)

In a uniform magnetic field, the net force on a current-carrying loop is zero. Hence, the loop cannot move. Using Fleming's left-hand rule, we find that a force acts in the radially outward direction throughout the circumference of the conducting loop.

Q 3 :

Two parallel wires in the plane of the paper are distance $X_{0}$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_{1}$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_{1}$ . In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_{2}$ . If $\frac{X_{0}}{X_{1}} = 3,$ the value of $\frac{R_{1}}{R_{2}}$ is [2014]

(3)

$\frac{m v^{2}}{R} = q v B \Rightarrow R = \frac{m v}{q B}$

$or R \propto \frac{1}{B}$ $[∵ m, q, v are the same]$

$∴$ $\frac{R_{1}}{R_{2}} = \frac{B_{2}}{B_{1}}$

$or, \frac{R_{1}}{R_{2}} = \frac{\frac{μ_{0}}{4 π} \times 2 I [\frac{1}{X_{1}} + \frac{1}{X_{0} - X_{1}}]}{\frac{μ_{0}}{4 π} \times 2 I [\frac{1}{X_{1}} - \frac{1}{X_{0} - X_{1}}]}$

$= \frac{(X_{0} - X_{1}) + X_{1}}{(X_{0} - X_{1}) - X_{1}} = \frac{X_{0}}{X_{0} - 2 X_{1}}$ $[Given \frac{X_{0}}{X_{1}} = 3]$

$∴$ $\frac{R_{1}}{R_{2}} = \frac{\frac{X_{0}}{X_{1}}}{\frac{X_{0}}{X_{1}} - 2} = \frac{3}{3 - 2} = 3$

Topic Question Set

Q 2 :

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to [2003]

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Topic Question Set

Q 2 : A conducting loop carrying a current I is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to [2003]

Want Us to Email you About Special Offers & Updates?

Q 2 :

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to [2003]