Question

A magnetic field of 0.1T forces a proton beam of 1.5 mA to move in a circle of radius 0.1 m. The plane of the circle is perpendicular to the magnetic field.

Of the following, which is the best estimate of the speed of a proton in the beam as it moves in the circle?

(A) 10^-2 m/s 

(B) 10³ m/s 

(C) 10⁶ m/s 

(D) 10⁸ m/s 

(E) 10¹⁵ m/s

Answer 1

The correct option is: (C) 10⁶ m/s 

Explanation:

Choose 1 proton moving in the circle. For this proton. F_net(C) = mv²/r    Fb = mv²/r

qvB = mv²/r     v = qBr/m = 1.6x10^–19 (0.1)(0.1) / (1.67x10^–27) ~ 10^–21 / 10^–27