Question

A wire of length l carries a current i long the x-axis. A magnetic field exists, which is given as `vecB = B_0 (veci + vecj + veck)`  T. Find the magnitude of the magnetic force acting on the wire.

Answer 1

Given:
A wire of length l cm
Electric current through the wire = i
Magnetic field, `vecB = B_0 (veci + vecj + veck)` T
As per the question, the current is passing along the X-axis.
Magnetic force,
`vecF = vecilxx vecB`
Putting the repective values in the above equation, we get:
= `i{(l veci)xx(B_0 veci + B_0  vecj + B_0 veck)}`

=`i{IB_0  veck - IB_0 vecj}`
the magnitude of the magnetic force,
`|vecF| = sqrt(2i^2l^2B_0^2)`
`therefore |vecF| = sqrt(2ilB_0