Question

An electron having charge $ 1.6\times {{10}^{-19}} $ and mass $ 9\times {{10}^{-31}}kg $ is moving with $ 4\times {{10}^{6}}m{{s}^{-1}} $ speed in a magnetic field $ 2\times {{10}^{-1}} $ tesla in a circular orbit. The force acting on electron and the radius of the circular orbit will be:

• A. $ 1.28\times {{10}^{-13}}N,\text{ }1.1\times {{10}^{-4}}m $
• B. $ 1.28\times {{10}^{-13~~}}N,\text{ }1.1\text{ }{{10}^{-3}}m $
• C. $ 1.28\times {{10}^{-14~}}N,\text{ }1.1\times {{10}^{-3}}m $
• D. $ 12.8\times {{10}^{-13~}}N,\text{ }1.1\times {{10}^{-4}}m $

Answer 1

Answer: (A)

From the relation $ F=qvB=1.6\times {{10}^{-19}}\times 4\times {{10}^{6}}\times 2\times {{10}^{-1}} $ $ =1.28\times {{10}^{-13}}N $ Radius of circular orbit is given by $ r=\frac{m\upsilon }{qB}=\frac{9\times {{10}^{-31}}\times 4\times {{10}^{6}}}{1.6\times {{10}^{-19}}\times 2\times {{10}^{-1}}} $ $ =1.1\times {{10}^{-4}}m $