Charge in an electric field: A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s2 , what is the charge that it carries?
A) 1.15 C
B) -1.15 C
C) 1150 C
D) -1150 C

Question

Charge in an electric field: A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C  . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s2  , what is the charge that it carries?
A) 1.15 C 
B) -1.15 C 
C) 1150 C 
D) -1150 C

Quizplus · Accepted Answer

We first need to find the net force acting on the sphere. The weight of the sphere is given by:
W = mg = (0.441 kg)(9.81 m/s^2) = 4.32 N
The electric force on the sphere is given by:
F = qE
where q is the charge on the sphere and E is the electric field. Since the electric field is in the vertical direction and the acceleration is in the horizontal direction, we can assume that the electric force does not contribute to the horizontal acceleration. Therefore, the net force in the horizontal direction is given by:
Fnet,x = ma = (0.441 kg)(13.0 m/s^2) = 5.733 N
Since the sphere is moving upward, we know that the net force in the vertical direction is:
Fnet,y = 4.32 N - qE = ma
Substituting in the values given, we get:
4.32 - qE = (0.441)(9.81)
-qE = (0.441)(9.81) - 4.32
qE = 2.163
q = 2.163/5.00 = 0.433 C
Therefore, the sphere carries a charge of 0.433 C, which is closest to choice A (1.15 C) after rounding to two significant figures.

Charge in an Electric Field: a Small Sphere with a Mass