Question

(a) An electron moves along a circle of radius $1$ m in a perpendicular magnetic field of strength $0.50T$. What would be its speed ? Is it reasonable ? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed ?

Answer 1

(a) $R=1m$, $B=0.5T$

$r=\frac{mv}{qB}$

$\Rightarrow 1=\frac{9.1\times {10}^{-31}\times v}{1.6\times {10}^{-19}\times 0.5}$

$\Rightarrow v=\frac{1.6\times 0.5\times {10}^{-19}}{9.1\times {10}^{-31}}=0.0879\times {10}^{10}\approx 8.8\times {10}^{10}m/s$

No, it is not reasonable as it is more than the speed of light.

$r=\frac{mv}{qB}$

$\Rightarrow 1=\frac{1.6\times {10}^{-27}\times v}{1.6\times {10}^{-19}\times 0.5}$

$\Rightarrow v=\frac{1.6\times {10}^{-19}\times 0.5}{1.6\times {10}^{-27}}=5\times {10}^2=5\times {10}^{7}m/s$