(A) The magnetic force per unit length between two long parallel wires is given by the formula:$F = \frac{\mu_0 i_1 i_2}{2 \pi d} = 2 \times 10^{-3} \

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(A) The magnetic force per unit length between two long parallel wires is given by the formula:$F = \frac{\mu_0 i_1 i_2}{2 \pi d} = 2 \times 10^{-3} \ N/m$When the currents are doubled ($i_1' = 2i_1$ and $i_2' = 2i_2$) and the separation is halved $(d' = d/2)$,the new force per unit length $F'$ is:$F' = \frac{\mu_0 (2i_1)(2i_2)}{2 \pi (d/2)}$$F' = \frac{4 \mu_0 i_1 i_2}{2 \pi (d/2)} = 8 \times \left( \frac{\mu_0 i_1 i_2}{2 \pi d} \right)$Substituting the initial value of force:$F' = 8 \times (2 \times 10^{-3} \ N/m) = 16 \times 10^{-3} \ N/m$Therefore,the new force per unit length is $16 \times 10^{-3} \ N/m$.

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

Medium

$A$ current of $10 \ A$ flows through two long parallel wires. The magnetic force per unit length on each wire is $2 \times 10^{-3} \ N/m$. If their currents are doubled and the separation between them is halved,then the magnetic force per unit length of each wire becomes $...... \times 10^{-3} \ N/m$.

A
$16$
B
$8$
C
$4$
D
$32$

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Moving Charges and Magnetism

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Force on a Current Carrying Conductor

As shown in the figure,a wire is bent to form a $D$-shaped loop carrying current $I$,where the curved part is a semi-circle of radius $R$. The loop is placed in a uniform magnetic field $\overrightarrow{B}$,which is directed into the plane of the paper. The net magnetic force on the closed loop is:

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Write the magnetic force equation on a current-carrying element $I\vec{dl}$ inside a magnetic field $\vec{B}$. Write the law used to determine the direction of the magnetic force.

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

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$A$ uniform magnetic field $\vec B = (3\hat i + 4\hat j + \hat k) \, T$ exists in a region of space. $A$ semicircular wire of radius $1 \, m$ carrying a current of $1 \, A$ has its centre at $(2, 2, 0)$ and is placed in the $x-y$ plane as shown in the figure. The force on the semicircular wire is:

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Three long,straight and parallel wires carrying currents are arranged as shown in the figure. The force experienced by $10\, cm$ length of wire $Q$ is

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As shown in the figure,a wire is bent to form a $D$-shaped loop carrying current $I$,where the curved part is a semi-circle of radius $R$. The loop is placed in a uniform magnetic field $\overrightarrow{B}$,which is directed into the plane of the paper. The net magnetic force on the closed loop is:

Write the magnetic force equation on a current-carrying element $I\vec{dl}$ inside a magnetic field $\vec{B}$. Write the law used to determine the direction of the magnetic force.

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

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