Question

A charged particle is moving in circular path of radius 100 meters in a uniform magnetic field. If mass of the charged particle is $9.1$ x ${10}^{-31}$ kg and its speed is 3 x ${10}^7$ m/s. Which of the following is the best estimate of the order of magnitude of the magnetic force needed to maintain this orbit?

• A. ${10}^{-22}$
• B. ${10}^{-17}$
• C. ${10}^{-10}$
• D. ${10}^{-6}$
• E. ${10}^{-2}$

Answer 1

The correct option is B ${10}^{-17}$

Given : $r=100$ m; $m=9.1\times {10}^{-31}$ kg; $v=3\times {10}^7$ m/s

Magnetic force $F=\frac{m{v}^2}{r}$
$=\frac{(9.1\times {10}^{-31})\times (3\times {10}^7{)}^2}{100}$
$=8.2\times {10}^{-18}\approx {10}^{-17}$ N