Question

A magnetic field of strength 1.0 T is produced by a strong electromagnet in a cylindrical region of radius 4.0 cm, as shown in the figure. A wire, carrying a  current of 2.0 A, is placed perpendicular to and intersecting the axis of the cylindrical region. Find the magnitude of the force acting on the wire.

Answer 1

Given:
Magnetic field, (B) = 1 T
Radius of the cylindrical region, r = 4.0 cm
Electric current through the wire, I = 2 A
The direction of magnetic field is perpendicular to the plane of the wire.
So, angle between wire and magnetic field, θ = 90˚
Magnetic force,
`vecF = i vecl xx vecB`
∴ `|vecF| = illBsintheta`
`|vecF| = ilBsin90°`
Here , l = 2r
∴ `|vecF| = i2rBsin90^circ`
= 2 × 8 ×10^-2 × 1.0 × 1
= 0.16N