An electron of mass "m" and charge "e" is moving in a circle of radius "r" with speed "v" in a uniform magnetic field strength "B".Then:

Explanation

To find the radius of the circular path of an electron in a magnetic field, equate the magnetic force to the centripetal force. The magnetic force on a moving charge is given by \(F = evB\), where 'e' is the charge, 'v' is the velocity, and 'B' is the magnetic field strength. The centripetal force required for circular motion is \(F = \frac{mv^2}{r}\), where 'm' is the mass of the electron and 'r' is the radius of the circle.Equating these forces gives:\(evB = \frac{mv^2}{r}\)Solving for 'r', we get:\(r = \frac{mv}{eB}\)This is the correct relationship between the radius and the other variables. The other options incorrectly rearrange or introduce irrelevant variables such as current 'I'.