Question

A 15000 V electron is describing a circle in a uniform magnetic field of induction 250 G acting at right angles to it. Calculate the radius of the circle.

a) 0.1 m
b) 0.2 m
c) 0.3 m
d) 0.4 m

Answer 1

To calculate the radius of the path of a 15,000 V electron in a 250 G magnetic field, apply the radius formula r = mv/(qB), after determining the electron's velocity through v = sqrt(2qV/m) where V equals the provided voltage.

Step-by-step explanation:

The question revolves around the concept of a charged particle, such as an electron, moving through a magnetic field and the resultant motion, which is typically circular if the magnetic field is perpendicular to the particle's velocity. To find the radius of the circle described by a 15,000 V electron in a 250 G (or 0.25 T) magnetic field, we use the formula for the radius r of the circular path, which is given by r = mv/(qB), where m is the electron mass (9.11 × 10-31 kg), v is the velocity of the electron, q is the charge of the electron (±e, with e = 1.60 × 10-19C), and B is the magnetic field strength.

First, we find the electron's velocity by equating the kinetic energy (KE) to the electric potential energy, KE = qV, where V is the potential difference the electron has been accelerated through. Solving for velocity, we get v = sqrt(2qV/m). Plugging in the values and solving for r, we get the radius of the circle in meters.