An electron moves in a magnetic field with a speed of \(3\times10^{6}\) m/s, in a circle of radius \(r\). If a proton also moves in a circle of the same radius in the region of same field, its speed will be approximately:
(Given: \(m_e = 9.1\times10^{-31}\) kg, \(m_p = 1.67\times10^{-27}\) kg)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(1.6\times10^{3}\) m/s
In a magnetic field a charge moves in a circle because the magnetic force provides the centripetal force.
\( \displaystyle qvB = \frac{mv^{2}}{r} \)
\( \displaystyle r = \frac{mv}{qB} \)
The electron and the proton have charges of the same magnitude and move in the same field on the same radius, so mv is the same for both.
\( \displaystyle m_p v_p = m_e v_e \)
\( \displaystyle v_p = \frac{m_e}{m_p}\,v_e \)
\( \displaystyle v_p = \frac{9.1\times10^{-31}\,\mathrm{kg}}{1.67\times10^{-27}\,\mathrm{kg}} \times 3\times10^{6}\,\mathrm{m/s} \)
\( \displaystyle v_p \approx 1.6\times10^{3}\,\mathrm{m/s} \)