(B) The magnetic force per unit length $f$ between two parallel wires carrying currents $I_1$ and $I_2$ separated by a distance $d$ is given by the fo

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(B) The magnetic force per unit length $f$ between two parallel wires carrying currents $I_1$ and $I_2$ separated by a distance $d$ is given by the formula:$f = \frac{\mu_0 I_1 I_2}{2\pi d}$In this rectangular loop,the current $I$ flows through both wires $PQ$ and $RS$. Therefore,$I_1 = I_2 = I$ (or $2I$ in the second case).Thus,the force per unit length is proportional to the square of the current: $f \propto I^2$.For the first case with current $I$,$f_{PQ}^{I} \propto I^2$.For the second case with current $2I$,$f_{PQ}^{2I} \propto (2I)^2 = 4I^2$.Taking the ratio:$\frac{f_{PQ}^{I}}{f_{PQ}^{2I}} = \frac{I^2}{4I^2} = \frac{1}{4}$.Therefore,the ratio is $1: 4$.

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

Medium

$A$ current-carrying rectangular loop $PQRS$ is made of uniform wire. The lengths are $PR = QS = 5\,cm$ and $PQ = RS = 100\,cm$. If the ammeter current reading changes from $I$ to $2I$,the ratio of magnetic forces per unit length on the wire $PQ$ due to wire $RS$ in the two cases respectively,$f_{PQ}^{I} : f_{PQ}^{2I}$,is:

JEE MAIN 2023 All JEE MAIN

A
$1: 2$
B
$1: 4$
C
$1: 5$
D
$1: 3$

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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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An arrangement of three parallel straight wires placed perpendicular to the plane of the paper carrying the same current $I$ along the same direction is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by:

MediumNEET 2017

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The magnetic field existing in a region is given by $\vec B = B_0 [1 + \frac{x}{l}] \hat k$. $A$ square loop of edge $l$ carrying current $I_0$ is placed with its edges parallel to the $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop.

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$A, B$ and $C$ are three parallel conductors of equal lengths and carry currents $I, I$ and $2I$ respectively as shown in the figure. The distance between $A$ and $B$ and between $B$ and $C$ is $d$. If $F_1$ is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $C$ on $A$,then:

DifficultMHT CET 2023

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Two wires $A$ and $B$ are carrying currents $I_1$ and $I_2$ as shown in the figure. The separation between them is $d$. $A$ third wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from $A$ such that the net force acting on it is zero. The possible values of $x$ are

MediumJEE MAIN 2019

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$A$ wire $X$ of length $50 \; cm$ carrying a current of $2 \; A$ is placed parallel to a long wire $Y$ of length $5 \; m$. The wire $Y$ carries a current of $3 \; A$. The distance between the two wires is $5 \; cm$ and the currents flow in the same direction. The force acting on the wire $X$ due to wire $Y$ is:

MediumJEE MAIN 2022

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