# 14.23 c) A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

The wire is lowered by a distance d=6cm.

In this case, the length of the wire inside the cylindrical region decreases.

Let this length be l.

$\\(\frac{l}{2})^{2}+d^{2}=r^{2}\\ \\(\frac{l}{2})^{2}=0.1^{2}-0.06^{2}\\ \\(\frac{l}{2})^{2}=0.01-0.0036\\ \\\\(\frac{l}{2})^{2}=0.0064\\ \\\frac{l}{2}=0.08\\ \\l=0.16m$

$\\F=BIlsin\theta \\ F=1.5\times 7\times 0.16$

F=1.68 N

This force acts in the vertically downward direction.

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