(C) The force $\vec{F}$ on a current-carrying wire is given by $\vec{F} = I(\vec{L} \times \vec{B})$.Here, $I = 1 \ A$, $\vec{L} = 0.5 \hat{i} \ m$, a

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$2 \ N$, along positive $z$-axis

(C) The force $\vec{F}$ on a current-carrying wire is given by $\vec{F} = I(\vec{L} \times \vec{B})$.Here, $I = 1 \ A$, $\vec{L} = 0.5 \hat{i} \ m$, and $\vec{B} = (2\hat{i} + 4\hat{j}) \ T$.Substituting the values:$\vec{F} = 1 \times (0.5 \hat{i} \times (2\hat{i} + 4\hat{j}))$$\vec{F} = 0.5 \times 2(\hat{i} \times \hat{i}) + 0.5 \times 4(\hat{i} \times \hat{j})$Since $\hat{i} \times \hat{i} = 0$ and $\hat{i} \times \hat{j} = \hat{k}$:$\vec{F} = 0 + 2\hat{k} = 2\hat{k} \ N$.The magnitude of the force is $|\vec{F}| = 2 \ N$, and the direction is along the positive $z$-axis.

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

Easy

$A$ current of $1 \ A$ is flowing along the positive $x$-axis through a straight wire of length $0.5 \ m$ placed in a region of a magnetic field given by $\vec{B} = (2\hat{i} + 4\hat{j}) \ T$. The magnitude and the direction of the force experienced by the wire are, respectively:

WBJEE 2013 All WBJEE

A
$\sqrt{18} \ N$, along positive $z$-axis
B
$\sqrt{20} \ N$, along positive $x$-axis
C
$2 \ N$, along positive $z$-axis
D
$4 \ N$, along positive $y$-axis

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Moving Charges and Magnetism

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Force on a Current Carrying Conductor

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$A$ square of side $2.0\,m$ is placed in a uniform magnetic field $B = 2.0\,T$ in a direction perpendicular to the plane of the square inwards. Equal current,$i = 3.0\,A$ is flowing in the direction shown in the figure. Find the magnitude of the magnetic force on the loop.

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$A$ conducting bar $PQ$ of length $l$ carrying current $I$ is suspended from a rigid support as shown in the figure. $A$ uniform magnetic field $B$ perpendicular to $PQ$ and directed away from the reader (into the plane) is applied. If the mass of the bar is $M$,find the tension in each string.

Medium

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When current passing through two parallel wires flows in the same direction,the force between them is $......$,while when current passes in opposite directions through the same wires,the force between them is $......$ (attraction,repulsion).

Medium

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Wires $1$ and $2$ carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?

MediumAIEEE 2002

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$A$ 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 $= 10\,cm$,$g = 10\,m/s^2$)

MediumJEE MAIN 2023

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$A$ current of $1 \ A$ is flowing along the positive $x$-axis through a straight wire of length $0.5 \ m$ placed in a region of a magnetic field given by $\vec{B} = (2\hat{i} + 4\hat{j}) \ T$. The magnitude and the direction of the force experienced by the wire are, respectively:

Similar Questions

$A$ square of side $2.0\,m$ is placed in a uniform magnetic field $B = 2.0\,T$ in a direction perpendicular to the plane of the square inwards. Equal current,$i = 3.0\,A$ is flowing in the direction shown in the figure. Find the magnitude of the magnetic force on the loop.

$A$ conducting bar $PQ$ of length $l$ carrying current $I$ is suspended from a rigid support as shown in the figure. $A$ uniform magnetic field $B$ perpendicular to $PQ$ and directed away from the reader (into the plane) is applied. If the mass of the bar is $M$,find the tension in each string.

When current passing through two parallel wires flows in the same direction,the force between them is $......$,while when current passes in opposite directions through the same wires,the force between them is $......$ (attraction,repulsion).

Wires $1$ and $2$ carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?

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