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Physics Question on Magnetic Force

An electron having charge 1.6 ×10−19 C1.6\,\times {{10}^{-19}}\,C and mass 9×10−31 kg9\times {{10}^{-31}}\,kg is moving with 4×106 kg4\times {{10}^{6}}\,kg speed in a magnetic field of 2×10−12\times {{10}^{-1}} tesla in a circular orbit. The force acting on an electron and the radius of circular orbit will be:

A

1.28 ×10−14 N,  1.1 ×10−3 m1.28\,\times {{10}^{-14}}\,N,\,\,1.1\,\times {{10}^{-3}}\,m

B

1.28 ×1015 N, 1.2 ×10−12m1.28\,\times {{10}^{15}}\,N,\,1.2\,\times {{10}^{-12}}m

C

1.28 ×10−13 N, 1.1 ×10−4 m1.28\,\times {{10}^{-13}}\,N,\,1.1\,\times {{10}^{-4}}\,m

D

none of these

Answer

1.28 ×10−13 N, 1.1 ×10−4 m1.28\,\times {{10}^{-13}}\,N,\,1.1\,\times {{10}^{-4}}\,m

Explanation

Solution

Force produced on an electron is given by F=eυB=1.6×10−19×4×106×2×10−1F=e\upsilon B=1.6\times {{10}^{-19}}\times 4\times {{10}^{6}}\times 2\times {{10}^{-1}} =1.28×10−13N=1.28\times {{10}^{-13}}N Since electron is moving in circular orbit So, mυ2r=eυB\frac{m{{\upsilon }^{2}}}{r}=e\upsilon B or r=mυeB=9×10−31×4×1061.6×10−19×2×10−1r=\frac{m\upsilon }{eB}=\frac{9\times {{10}^{-31}}\times 4\times {{10}^{6}}}{1.6\times {{10}^{-19}}\times 2\times {{10}^{-1}}} =1.1×10−4m=1.1\times {{10}^{-4}}m