Question

Suppose a wire is kept horizontal, through which current $i=10\sin \omega t$ is flowing. A uniform magnetic field of $50\text{T}$ exist in vertical direction. The average magnetic force on the wire in a complete cycle of current will be -

• A. $10\text{N}$
• B. $20\text{N}$
• C. $30\text{N}$
• D. $0\text{N}$

Answer 1

The correct option is D $0\text{N}$

We know that, magnetic force on a current carrying wire is given by,

$\overrightarrow{F}=I(\overrightarrow{l}\times \overrightarrow{B})$

Here, length of wire $l$ and magnetic field $B$ is independent of time.

So, average magnetic force depends on average value of current.

And average value of current for a sinusoidal current is zero in a full cycle.

Hence, average magnetic force on the wire is zero for a full cycle of current.