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

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 $r=\frac{m\upsilon }{qB}=\frac{9\times {10}^{-31}\times 4\times {10}^6}{1.6\times {10}^{-19}\times 2\times {10}^{-1}}$ $=1.1\times {10}^{-4}m$