Question

Doubly ionized helium ions are projected with a speed of $10km{s}^{-1}$ in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find (a) the force acting on an ion, (b) the radius of the circle in which it circulates and (c) the time taken by an ion to complete the circle.

Answer 1

$V={10}^{4}m/s,B=1.0T,q=2C$

$\left(a\right)F=qVB$

$=2\times 1.6\times {10}^{-19}\times {10}^4\times 1.0$

$=3.2\times {10}^{-15}N$

$\left(b\right)r=\frac{mV}{qB}=\frac{2\times {10}^{-23}}{{10}^{-19}}$

$=2\times {10}^{-4}m$

$\left(c\right)T=\frac{2\pi r}{V}=\frac{6.28\times 2.1\times {10}^{-4}}{{10}^4}$

$=1.31\times {10}^{-7}S$