A proton moving in perpendicular magnetic field possess energy ‘ E ‘. The magnetic field is increased four times. But the proton is constrained to move in the path of same radius. The kinetic energy will increase
A) 16 times.
B) 8 times.
C) 2 times.
D) 4 times.
A proton moving in perpendicular magnetic field possess energy ‘ E ‘. The magnetic field is increased four times. But the proton is constrained to move in the path of same radius. The kinetic energy will increase
A) 16 times.
B) 8 times.
C) 2 times.
D) 4 times.

Correct option is A.

Radius,
\begin{aligned} R &=\frac{m v}{9 B}=\frac{\sqrt{m} \sqrt{m} v^{2}}{9 B} \\ &=\frac{\sqrt{m} \sqrt{E}}{9 B} \end{aligned}
if B \rightarrow 4 B.
R=\frac{\sqrt{m} \sqrt{E_{2}}}{9\times 4 B}
\frac{\sqrt{m} \sqrt{E}}{9 B}=\frac{\sqrt{m} \sqrt{E_{2}}}{9(4 B)}
\sqrt{E}_{2}=4 \sqrt{E}
E=16 E inereased