Question

A proton and an electron are moving at the same velocity perpendicularly to a constant magnetic field.

(a) How do the magnitudes of the magnetic forces on them compare? Explain

(b) What about the magnitudes of their accelerations? Explain

Answer 1

Answers :

As we know :

Charge of Electron (q_e) = - e = - 1.6 x 10^-19 C

Charge of Proton (q_p) = + e = + 1.6 x 10^-19 C

Mass of Electron (m_e) = 9.1 x 10^-31 kg

Mass of Proton (m_e) = 1.67 x 10^-27 kg

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Part (a) Answer :

Since, Force on a moving charge in a magnetic field is given by : F = q [ v x B ]

Where, q is charge on the particle

v is the speed of the particle

and, B is strength of the magnetic field.

Here, v and B is same for both the electron and the proton.

Thus, Force acting on these charges will be directly proportional to the charge of the particles.

But, The magnitude of charge on Electron and the Proton is same (q_e = q_p = e).

Therefore, The magnitude of forces on both the electron and the proton will be same (F_e = F_p). But, the direction of force on both the charges will be opposite to each other.

.

Part (b) Answer :

Now, Acceleration of the charges will be given by : a = F / m

Here The magnitude of forces on both the electron and the proton will be same. Therefore, The acceleration of the particle will be inversely proportional to the mass of the particles.

Here, m_proton > m_electron

Therefore, Acceleration of electron will be greater than the acceleration of the proton.