Name: Magnetic Flux
Uploaded: 2019-07-19
Duration: 6 min 44 s
Description: Magnetic flux is the total number of magnetic lines of force that are passing through a given surface. To learn more about this intriguing concept, watch the...

Question

A uniform magnetic field acts on rectangular current loop, being perpendicular to the plane of the loop. Show that it experiences no net force. What is effect of the magnetic force on the loop?

Accepted Answer

Consider a rectangular loop $A B C D$ and magnetic moment vector $\vec{m}$ makes an angle $θ$ with magnetic field $\vec{B}$ .

Taken side $A D$ and $B C$ with current in opposite directions.

Now, force on side $A D$ is ${\vec{F}}_{AD} = I \int_{AD} d \vec{l} \times \vec{B}$ .

Here, $\vec{B}$ is constant and $\int d \vec{l}$ is sum of infinitesimal length vectors along $A D$ in current direction.

$∴ \int d \vec{l} = \vec{A D}$

$∴ {\vec{F}}_{AD} = I \times \vec{A D} \times \vec{B}$ .

Similarly, we have,

${\vec{F}}_{B C} = I \times \vec{B C} \times \vec{B} ∴ {\vec{F}}_{A D} + {\vec{F}}_{B C} = I (\vec{A D} + \vec{C B}) \times \vec{B}$

$\vec{A D} + \vec{C D} = 0$ (equal and opposite vectors)

Similarly, forces on sides $A B$ and $D C$ also cancel. So, total force on the loop is $\vec{F} = 0$ .

When current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a shaft.

A uniform magnetic field acts on rectangular current loop, being perpendicular to the plane of the loop. Show that it experiences no net force. What is effect of the magnetic force on the loop?

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