Answer:
Time spent by the charge in the magnetic field = 0.008445 s = (8.445 × 10⁻³) s
Explanation:
The force exerted on the charge due to magnetic field = the centripetal force that causes the charge to move in a circular motion.
Force due to magnetic field = qvB sin θ
q = charge on the particle = 8.6 μC
v = velocity of the charge
B = magnetic field strength = 3.2 T
θ = angle between the velocity of the charge and the magnetic field = 90°, sin 90° = 1
F = qvB
Centripetal force responsible for circular motion = mv²/r = mvw
where w = angular velocity.
mvw = qvB
mw = qB
w = (qB/m) = (8.6 × 10⁻⁶ × 3.2)/(7.4 × 10⁻⁸)
w = 3.72 × 10² rad/s
w = 372 rad/s
w = (angular displacement)/time
Time = (angular displacement)/w
Angular displacement = π rads (half of a circle; 2π/2)
Time = (π/372) = 0.008445 s
