(A) The 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

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$6 \times 10^{-7} \text{ N m}^{-1}$ repulsive

(A) The 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:$f = \frac{\mu_0}{4\pi} \frac{2 I_1 I_2}{d}$Given values are $I_1 = 1 \text{ A}$,$I_2 = 3 \text{ A}$,$d = 1 \text{ m}$,and $\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m A}^{-1}$.Substituting these values into the formula:$f = 10^{-7} \times \frac{2 \times 1 \times 3}{1} = 6 \times 10^{-7} \text{ N m}^{-1}$Since the currents flow in opposite directions,the force between the wires is repulsive.Therefore,the force per unit length is $6 \times 10^{-7} \text{ N m}^{-1}$ and it is repulsive.

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

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Two parallel wires $1 \text{ m}$ apart carry currents of $1 \text{ A}$ and $3 \text{ A}$ respectively in opposite directions. The force per unit length acting between these two wires is

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A
$6 \times 10^{-7} \text{ N m}^{-1}$ repulsive
B
$6 \times 10^{-7} \text{ N m}^{-1}$ attractive
C
$6 \times 10^{-5} \text{ N m}^{-1}$ repulsive
D
$6 \times 10^{-5} \text{ N m}^{-1}$ attractive

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Moving Charges and Magnetism

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Force on a Current Carrying Conductor

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$A$ straight wire is placed in a magnetic field that varies with distance $x$ from the origin as $\vec{B} = B_0 \left( 2 - \frac{x}{a} \right) \hat{k}$. The ends of the wire are at $(a, 0)$ and $(2a, 0)$ and it carries a current $I$ in the positive $x$-direction. If the force on the wire is $\vec{F} = IB_0 \left( \frac{ka}{2} \right) \hat{j}$, then the value of $k$ is:

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The wires which connect the battery of an automobile to its starting motor carry a current of $300\; A$ (for a short time). What is the force per unit length between the wires if they are $70\; cm$ long and $1.5\; cm$ apart? Is the force attractive or repulsive?

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The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x) \hat{k} \text{ T}$. $A$ square loop of edge $50 \text{ cm}$ carrying $0.5 \text{ A}$ current is placed in the $x-y$ plane with its edges parallel to the $x-y$ axes,as shown in the figure. The magnitude of the net magnetic force experienced by the loop is . . . . . . $\text{mN}$.

DifficultJEE MAIN 2024

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$A$ rectangular loop of wire,supporting a mass $m$,hangs with one end in a uniform magnetic field $\overrightarrow{B}$ pointing into the plane of the paper. $A$ clockwise current $i$ is set up such that $i > mg/Ba$,where $a$ is the width of the loop. Then:

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If a wire of length $1\, m$ is placed in a uniform magnetic field of $1.5\, T$ at an angle of ${30^\circ}$ with the magnetic field,and the current in the wire is $10\, A$,then the force on the wire will be.......$N$. (in $.5$)

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Two parallel wires $1 \text{ m}$ apart carry currents of $1 \text{ A}$ and $3 \text{ A}$ respectively in opposite directions. The force per unit length acting between these two wires is

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The wires which connect the battery of an automobile to its starting motor carry a current of $300\; A$ (for a short time). What is the force per unit length between the wires if they are $70\; cm$ long and $1.5\; cm$ apart? Is the force attractive or repulsive?

$A$ rectangular loop of wire,supporting a mass $m$,hangs with one end in a uniform magnetic field $\overrightarrow{B}$ pointing into the plane of the paper. $A$ clockwise current $i$ is set up such that $i > mg/Ba$,where $a$ is the width of the loop. Then:

If a wire of length $1\, m$ is placed in a uniform magnetic field of $1.5\, T$ at an angle of ${30^\circ}$ with the magnetic field,and the current in the wire is $10\, A$,then the force on the wire will be.......$N$. (in $.5$)

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