A laboratory electromagnet produces a magnetic field of magnitude 1.43 T. A prot

Question

A laboratory electromagnet produces a magnetic field of magnitude 1.43 T. A proton moves through this field with a speed of 5.96 ? 106 m/s.

(a) Find the magnitude of the maximum magnetic force that could be exerted on the proton.

(b) What is the magnitude of the maximum acceleration of the proton?

(c) Would the field exert the same magnetic force on an electron moving through the field with the same speed? (Assume that the electron is moving in the same direction as the proton.)

(d) Would the electron undergo the same acceleration?

Explanation / Answer

(a)
Magnetic force, F = q * (v x B)
F = qvBsin(theta)
(theta = angle between v and B).
Maximum magnetic force the angle is 90 degree and sin (90) = 1 then
F = q*v*B = 1.6*10^(-19) * 5.96 * 10^6 * 1.43
F = 1.364 x 10-12 N

(b)
The resultant force is the centripetal force so
F = m*a
mass of proton = 1.67 * 10^-27
a = F/m = 1.364 * 10^-12 / 1.67 * 10^-27
a = 8.2 * 10^14 m/s2

(c)
Yes because the charge on proton and electron is same. so the force will be same.

(d)
Not because the electron has a mass much smaller than the proton.

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