Question

An electron at rest has a charge of $1.6\times {10}^{-19}C$. It starts moving with a velocity $v=c/2$, where $c$ is the speed of light, then the value the new charge on it is-

• A. $1.6\times {10}^{-19}$ Coulomb
• B. $1.6\times {10}^{-19}\sqrt{1-{\left(\frac{1}{2}\right)}^2}$ Coulomb
• C. $1.6\times {10}^{-19}\sqrt{{\left(\frac{1}{2}\right)}^2-1}$ Coulomb
• D. $\frac{1.6\times {10}^{-19}}{\sqrt{1-{\left(\frac{1}{2}\right)}^2}}$ Coulomb
  

Answer 1

The correct option is A $1.6\times {10}^{-19}$ Coulomb

• $\text{From the property of invariance of electric charge :}$ The magnitude of the charge on a body does not vary with speed or frame of reference.

i.e Magnitude of Charge at rest = Charge in motion

• $q_{rest}=1.6\times {10}^{-19}C$ (given)

Therefore electron charge in motion will also be same $q=1.6{\times }^{-19}C$

• Hence, Option(A) is correct.