29.20. Review. A 0.03 kg metal ball having net charge Q = 5.00 C is thrown out o

Question

29.20. Review. A 0.03 kg metal ball having net charge Q = 5.00 C is thrown out of a window horizontally north with a speed ofv = 20.0 m/s. The window is at a height h = 20.0 m above the ground. A uniform, horizontal magnetic field of magnitude B = 0.0100 T is perpendicular to the plane of the ball's trajectory and directed toward the west. (a) Assuming the ball follows the same trajectory as it would in the absence of the magnetic field, find the magnetic force acting on the ball just before it hits the ground. (b) Based on the result of part (a), is it justified for three-significant-digit precision to assume the trajectory is unaffected by the magnetic filed? Explain. 0

Explanation / Answer

Given,

Q = 5 uC ; vx = 20 m/s ; h = 20 m ; B = 0.01 T

a)We know that,

F = q v B

we have, vx = 20 m/s

We need to know the vertical velocity

vy = sqrt (2 g h) = sqrt (2 x 9.81 x 20) = 19.81 m/s

V = sqrt (20^2 + 19.81^2) = 28.15 m/s

F = q V B = 5 x 10^-6 x 28.15 x 0.01 = 1.408 x 10^-6 N

Hence, F = 1.408 x 10^-6 N

b)No, since the B field will definately get a change in the trajectory of the ball, although the speed remains unaffected.

q v B = m v^2/R

R = m v^2/F = 0.03 x 28.18^2/1.408 x 10^-6 = 1.688 x 10^7 m

Very large radius.

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