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 $1.0$ Tesla find:

A)the force acting on the ion.

B)The radius of the circle in which it circulates.

C)The time is taken by an ion to complete the circle.

Answer 1

Given:

$V=10Km/s={10}^{4}m/s$

$B=1T,q=2e$

(a) $F=qVB=2\times 1.6\times {10}^{-19}\times {10}^4\times 1=3.2\times {10}^{-15}N$

(b) $r=\frac{mV}{qB}=\frac{4\times 1.6\times {10}^{-27}\times {10}^4}{2\times 1.6\times {10}^{-19}\times 1}=2\times \frac{{10}^{-23}}{{10}^{-19}}=2\times {10}^{-4}m$

(c) Time taken $=\frac{2\pi r}{V}=\frac{2\pi mv}{qB\times v}=\frac{2\pi \times 4\times 1.6\times {10}^{-27}}{2\times 1.6\times {10}^{-19}\times 1}$

$=4\pi \times {10}^{-8}=4\times 3.14\times {10}^{-8}=12.56\times {10}^{-8}=1.256\times {10}^{-7}sec$.