Question Detail
Question
A metal ball of 10kg with 5 C charges is moving perpendicular to the magnetic field of 5T. The radius of the path is 80 m. What is the speed of the ball and the period of the ball?
Correct Answer
Option D is the correct answer.
Detailed Explanation
When a charged particle moves perpendicular to a magnetic field, the magnetic force provides the centripetal force for circular motion.Magnetic force (FB) = qvBCentripetal force (Fc) = mv²/rEquating them: qvB = mv²/rSolving for speed (v): v = qBr / mGiven: m = 10 kg, q = 5 C, B = 5 T, r = 80 m.v = (5 C * 5 T * 80 m) / 10 kg = 25 * 80 / 10 = 25 * 8 = 200 m/s.Now, calculate the period (T) of the circular motion:T = 2πr / vT = (2π * 80 m) / (200 m/s) = 160π / 200 = 0.8π s ≈ 0.8 * 3.14159 ≈ 2.513 s.So, the speed is 200 m/s and the period is approximately 2.5 s.
Hint
Equate the magnetic force on the charged particle to the centripetal force. Then use the relationship between radius, speed, and period for circular motion.