Two objects of identical mass but opposite sign of charge maintain a separation in
distance due to a constant external electric field that points to the left.
A. What is the sign of the charge on the right?
Negative. If there were no external electric field, the charges would attract each other.
The electric field causes the separation of the charges, so it has to produce a force to the
right for the charge on the right and a force to the left for the charge on the left. For this
to occur the charge on the right has to be negative and the charge on the left has to be
positive: 𝐹⃑𝑒 = 𝑞𝐸⃑⃑ .
B. State whether the following—if it is the only quantity that changes—has to increase
or decrease if the angle (θ) is observed to increase.
1. the magnitude of the electric field.
Increase. An increase in |𝐸⃑⃑ | increases 𝐹⃑𝐸 that points away from the center
line on either charge. The angle will increase. *See the free-body diagram for
the right object below.
2. the magnitude of the charge.
Decrease. A decrease in the magnitude of the charge decreases the electrical
force of attraction between the two objects. The angle will increase.
3. the length of both strings.
Increase. Imagine the length of both strings getting longer but maintaining the
initial angle. The separation distance between both charges will increase, so
their force of attraction will decrease. The angle will increase.
4. the mass of both objects.
Decrease. A decrease in the mass reduces the gravitational force which
decreases the string tension. The horizontal component of the tension that
pulls the two objects toward the centerline will decrease. The angle will
increase.
θ θ