A 170g model airplane charged to 174 mC and traveling at 30

A 170-g model airplane charged to 17.4 mC and traveling at 3.0 m/s passes within 8.4 cm of a wire, nearly parallel to its path, carrying a 45-A current. What acceleration (in g\'s) does this interaction give the airplane? Express your answer using two significant figures.

Solution

Magnetic field due to wire at the position of plane (r = 8.4 cm = 0.084 m )

B = u0 I / (2 pi r)

B = (4 x pi x 10^-7 x 45 ) / (2 x pi x 0.084 )

B = 1.071 x 10^-4 T

and magnetic force on moving charge

Fb = q ( v x B)

Fb = (17.4 x 10^-3 ) ( 3 x 1.071 x 10^-4)

Fb = 5.593 x 10^-6 N

and a = Fb / m = 5.593 x 10^-6 / 0.170 = 3.29 x 10^-5 m/s^2

a( in g) = (3.29 x 10^-5) / 9.8 = 3.36 x 10^-6 g ..........Ans