Question

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the inflence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path , then the mass of the particle is (Given charge of electron =$1.6\times {10}^{-19}C$)

• A. $1.6\times {10}^{-19}kg$
• B. $1.6\times {10}^{-27}kg$
• C. $9.1\times {10}^{-31}kg$
• D. $2.0\times {10}^{-24}kg$

Answer 1

The correct option is D $2.0\times {10}^{-24}kg$

Given: Radius of the circular path= $0.5cm$

Magnetic field = $0.5T$

Electric field= $100V/m$

Solution: For a body to move in a circular path,

centripetal force= electromagnetive force

According to the question,

$\frac{m{v}^2}{r}=qvB$

where, v is the velocity of the electron.

$mv=qBr$ (1)

Also, we know that $v=\frac{E}{B}$

substituting the value of velocity in equation (1) we get,

$m=\frac{qR{B}^2}{E}$

putting the values we get,

$m=2\times {10}^{-24}$

Hence, the correct option is (D).