(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

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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:

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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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$A$ 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

The figure shows an equilateral triangle $ABC$ of side length '$l$' carrying currents as shown,placed in a uniform magnetic field '$B$' perpendicular to the plane of the triangle. The magnitude of the net magnetic force on the triangle is:

Two long wires with no contact are placed perpendicular to each other. $i_1$ and $i_2$ are currents flowing through these wires respectively. The magnetic force on a small length '$d$' of the second wire situated at a distance '$l$' from the first wire is proportional to,

$A$ circular conducting loop of radius $R$ carries a current $I$. Another straight infinite conductor carrying current $I$ passes through the diameter of this loop as shown in the figure. The magnitude of the force exerted by the straight conductor on the loop is:

Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases,which type of force acts between the two wires?

Two thin long parallel wires, $W_1$ and $W_2$ separated by distance '$a$',carry currents $i$ and $3i$ respectively in the same direction. The magnitude of the force per unit length exerted by wire $W_1$ on wire $W_2$ is

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