(D) The magnetic force $F_m$ acting on the side of the loop inside the magnetic field must balance the weight $mg$ of the mass.$F_m = mg$Since $F_m =

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(D) The magnetic force $F_m$ acting on the side of the loop inside the magnetic field must balance the weight $mg$ of the mass.$F_m = mg$Since $F_m = ILB$,we have $ILB = mg$.Using Ohm's law,$I = \frac{V}{R}$,so the equation becomes $\left(\frac{V}{R}\right)LB = mg$.Rearranging for $V$,we get $V = \frac{mgR}{LB}$.Given values:$m = 1\,g = 10^{-3}\,kg$$g = 10\,m/s^2$$R = 10\,\Omega$$L = 10\,cm = 0.1\,m$$B = 10^3\,G = 10^3 \times 10^{-4}\,T = 0.1\,T$Substituting these values:$V = \frac{(10^{-3}\,kg)(10\,m/s^2)(10\,\Omega)}{(0.1\,m)(0.1\,T)} = \frac{10^{-1}}{10^{-2}} = 10\,V$.

Class 12 Physics Moving Charges and Magnetism Force on a Current Carrying Conductor

Medium

$A$ massless square loop of wire with resistance $10\,\Omega$ supports a mass of $1\,g$. It hangs vertically with one of its sides in a uniform magnetic field of $10^3\,G$,directed outwards in the shaded region. $A$ $DC$ voltage $V$ is applied to the loop. For what value of $V$ will the magnetic force exactly balance the weight of the supporting mass of $1\,g$? (Given: side length of the loop $= 10\,cm$,$g = 10\,m/s^2$)

JEE MAIN 2023 All JEE MAIN

A
$\frac{1}{10}\,V$
B
$1\,V$
C
$100\,V$
D
$10\,V$

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Class 12

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Moving Charges and Magnetism

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Force on a Current Carrying Conductor

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$A$ square loop of length $L$ is placed with its edges parallel to the $XY$-axes. The loop carries a current $I$. If the magnetic field in the region varies as $B = B_0 \left(1 + \frac{xy}{L^2}\right) \hat{k}$, then the magnitude of the net force on the loop will be:

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$A$ long wire $AB$ is placed on a table. Another wire $PQ$ of mass $1.0\, g$ and length $50\, cm$ is set to slide on two rails $PS$ and $QR$. $A$ current of $50\, A$ is passed through the wires. At what distance above $AB$ will the wire $PQ$ be in equilibrium? (in $mm$)

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$A$ rectangular coil $ABCD$ is hung from one side of a balance as shown in the figure. $A$ $500 \, g$ mass is added to the other arm to balance the weight of the coil. $A$ current of $9.8 \, A$ is passed through the coil and a constant magnetic field of $0.4 \, T$ acting inward is switched on such that only arm $CD$ of length $1.5 \, cm$ lies in the field. The additional mass $m$ that must be added to regain the balance is: (in $, g$)

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The figure shows three long straight wires $P, Q$ and $R$ carrying currents normal to the plane of the paper. All three currents have the same magnitude. Which arrow best shows the direction of the resultant force on the wire $P$?

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$A$ square loop of length $L$ is placed with its edges parallel to the $XY$-axes. The loop carries a current $I$. If the magnetic field in the region varies as $B = B_0 \left(1 + \frac{xy}{L^2}\right) \hat{k}$, then the magnitude of the net force on the loop will be:

Equal currents are passing through two very long and straight parallel wires in the same direction. They will . . . . . . .

$A$ long wire $AB$ is placed on a table. Another wire $PQ$ of mass $1.0\, g$ and length $50\, cm$ is set to slide on two rails $PS$ and $QR$. $A$ current of $50\, A$ is passed through the wires. At what distance above $AB$ will the wire $PQ$ be in equilibrium? (in $mm$)

The figure shows three long straight wires $P, Q$ and $R$ carrying currents normal to the plane of the paper. All three currents have the same magnitude. Which arrow best shows the direction of the resultant force on the wire $P$?

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