Question

When an electron is accelerated through a potential difference V,it experiences a force F through a uniform transverse magnetic field.If the potential difference is increased to 2 V,the force experienced by the electron in the same magnetic field is

• A. $2F$
• B. $2\sqrt{2}F$
• C. $\sqrt{2}F$
• D. $4F$

Answer 1

Answer: (C)

$\sqrt{2}F$

If a charge particle is accelerated through V potential its kinetic energy is $\frac{P^2}{2m}=eV$

If the accelerating potential is doubled it's momentum hence speed is increased by $\sqrt{2}$

$\frac{P_1^2}{P_2^2}=\frac{eV}{e2V}=\frac{1}{2}$

$P_2=\sqrt{2}{P}_1$

$v_2=\sqrt{2}{v}_1$

The magnetic force is given by $F=q(V\times B)$

Since velocity is increased by $\sqrt{2}$ force will be increased by $\sqrt{2}$.

The magnetic force will be $\sqrt{2}F$