# Calculating Torque of charges at an angle

1. Homework Statement
A thin wooden stick of length 12 cm has a tiny metal sphere
glued to each end. A charge of +3 microC is placed on one
sphere and a charge of -2 microC is placed on the other.
The center of mass is located 7 cm from the positively-
charged sphere. The system is mounted on a fixed
horizontal E-W axle passing through the center of mass
about which the system is free to rotate with no friction.
When the system is then placed in a horizontal uniform
southward electric field of 800 N/C, the resulting
equilibrium position of the system is horizontal with
the positive charge due S of the negative charge.

What amount of torque (about the axle) is required
to hold the system at an angular displacement of 25
degrees away from the equilibrium position?

2. Homework Equations
torque = LqEsin(theta)

3. The Attempt at a Solution
I tired plugging in the values into the equation:

torque = (0.12)(1x10^-6)(800)(sin(25)) but it isn't coming out right. What am I doing wrong?

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collinsmark
Homework Helper
Gold Member
Hello Pete_01,

I tired plugging in the values into the equation:

torque = (0.12)(1x10^-6)(800)(sin(25)) but it isn't coming out right. What am I doing wrong?
Rather than just plug some numbers into an equation, I suggest taking a step back and think about what that equation means, and in what situations it is applicable.

The problem statement gives you two charges, one of 3 μC on one side of the stick, and -2 μC on the other. Since the spheres are oppositely charged, the electric forces obviously point in opposite directions. But when it comes to their corresponding torques on the stick, are the torques working together or against each other? (Hint: the spheres are oppositely charged, yes. But the spheres are also on opposite sides of the same stick!)

It doesn't quite end there. The center of mass (where the axle is located) is not at the center of the stick. The positively charged sphere is 7 cm from the axle, meaning the negatively charged sphere is 5 cm from the axle. How does all of this affect the torques involved?