Question Detail
Question
What must the charge (sign and magnitude) of a particle of mass 5 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 800 N/C?
Correct Answer
Option B is the correct answer.
Detailed Explanation
For the particle to remain stationary, the electric force (Fe) must balance the gravitational force (Fg). The gravitational force acts downward (Fg = mg). Since the electric field is directed downward, for the electric force to counteract gravity and be upward, the charge (q) must be negative.Fe = Fg => qE = mgq = mg / EGiven:Mass m = 5 g = 5 × 10-3 kgElectric field E = 800 N/CAcceleration due to gravity g = 9.8 m/s2q = (5 × 10-3 kg × 9.8 m/s2) / 800 N/Cq = 0.049 N / 800 N/Cq = 0.00006125 C = 61.25 × 10-6 C = 61.25 µCSince the charge must be negative, q = -61.25 µC. The closest option is -61.3 µC (assuming µF is a typo for µC).
Hint
For an object to remain stationary in an electric field, the electric force must balance the gravitational force. Consider the direction of forces and the sign of the charge.