Magnetic Effects Of Current Question 290
Question: An electron having charge $ 1.6\times {{10}^{-19}},C $ 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 [MP PET 1996; JIPMER 2000; BVP 2003]
Options:
A) $ 12.8\times {{10}^{-13}}N,,1.1\times {{10}^{-4}}m $
B) $ 1.28\times {{10}^{-14}}N,,1.1\times {{10}^{-3}}m $
C) $ 1.28\times {{10}^{-13}}N,,1.1\times {{10}^{-3}}m $
D) $ 1.28\times {{10}^{-13}}N,,1.1\times {{10}^{-4}}m $
Show Answer
Answer:
Correct Answer: D
Solution:
F = evB $ =1.6\times {{10}^{-19}}\times 4\times 10^{6}\times 2\times {{10}^{-1}} $ $ =1.28\times {{10}^{-13}}N $ Also $ \frac{mv^{2}}{r}=evB\Rightarrow r=\frac{mv}{eB} $
$ \Rightarrow \ r=\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 $
BETA
