Question

A cyclotron designed to speed up protons which has a magnetic field of 0.8 Tesla over a region of radius 1.6 m, then maximum speed of protons $(q=1.6\times {10}^{-19}C,m=1.6\times {10}^{-27}kg)$

• A. $128\times {10}^{6}m/s$
• B. $128\times {10}^{3}m/s$
• C. $32\times {10}^{6}m/s$
• D. $32\times {10}^{3}m/s$

Answer 1

The correct option is D $32\times {10}^{3}m/s$

$r=\frac{mv}{qB};v=\frac{qBr}{m}$
=$\frac{1.6\times {10}^{-19}\times 0.8\times 1.6}{1.6\times {10}^{-27}}$
$=1.6\times 0.8\times {10}^8=16\times 8\times {10}^6$
$=128\times {10}^{6}m/s$