# A Wire of Length L Carries a Current I Long the X-axis. a Magnetic Field Exists, Which is Given as - Physics

Sum

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.

#### Solution

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

Concept: Force on a Current - Carrying Conductor in a Uniform Magnetic Field
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 12 Magnetic Field
Q 10 | Page 231