A particle of mass m has an electric charge q. This particle is accelerated through a potential difference V and then enters normally into a uniform magnetic field B. It performs circular motion of radius R. The ratio of its charge to its mass, q/m — also called the specific charge — is .

Question

Accepted Answer

(1) (2V)/(B²R²). Given: the particle starts from rest, is accelerated through V, then enters a field B at right angles and moves on a circle of radius R. Idea: the accelerating stage fixes the speed and the magnetic stage fixes the radius; eliminate v between the two. Energy gained: qV=1/2mv², so v=√(2qV)/m. In the field: qvB=(mv²)/R, so v=(qBR)/m. Equating the two and squaring: (2qV)/m=(q²B²R²)/(m²), which gives q/m=(2V)/(B²R²).

A particle of mass m has an electric charge q. This particle is accelerated through a potential difference V and then enters normally into a uniform magnetic field B. It performs circular motion of radius R. The ratio of its charge to its mass, q/m — also called the specific charge — is ______.

Step-by-step solution

Why the other options are wrong