A wire carrying a current I along the positive x-axis has length L . It is kept in a magnetic field B → = 2 i ^ + 3 j ^ - 4 k ^ T . The magnitude of the magnetic force acting on the wire is:

Question

Aicharya · Accepted Answer

The formula to calculate the magnetic force acting on the wire is given by

$\vec{F} = I \vec{L} \times \vec{B} . . . (1)$

As the length of the wire is along positive x-axis, it can be written that

$\vec{L} = L \hat{i} . . . (2)$

Substitute the expressions of the required parameters into equation (2) to obtain the force.

$\begin{array}{rcl} \vec{F} & = & I L \hat{i} \times (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) \\ = & 3 I L \hat{k} + 4 I L \hat{j} . . . (3) \end{array}$

Hence, the magnitude of the force can be written as

$\begin{array}{rcl} F & = & \sqrt{{(3 I L)}^{2} + {(4 I L)}^{2}} \\ = & 5 I L \end{array}$

A wire carrying a current I along the positive x-axis has length L . It is kept in a magnetic field B → = 2…

Solution