hmparticle9
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- Homework Statement
- Two identical equally charged pith balls of mass ##m## and negligible radius are hanging from the same point on strings of length ##L##. The strings have an angle ##\theta## between them. What is the charge on each and the electric force on each ball?
- Relevant Equations
- $$F = \frac{q^2}{4\pi \epsilon_0 4 L^2 \sin^2 \frac{\theta}{2}}$$
The force is easily found to be:
$$F = \frac{q^2}{4\pi \epsilon_0 4 L^2 \sin^2 \frac{\theta}{2}}$$
I am trying to think how to get the charge ##q## from this. Since the balls are stationary the force felt on each of the balls must equal the force of gravity on the balls:
The force of gravity on the balls is ##mg \sin \frac{\theta}{2} ##.
However, if I set ##F## equal to this I do not get the answer in the book. The answer in the book is
$$\sqrt{(mg) \tan \frac{\theta}{2}4\pi \epsilon_0 4 L^2 \sin^2 \frac{\theta}{2}}$$
This,to me, suggests that the force on the ball is given by ##(mg) \tan \frac{\theta}{2}##. Could someone explain to me why this is the case?
$$F = \frac{q^2}{4\pi \epsilon_0 4 L^2 \sin^2 \frac{\theta}{2}}$$
I am trying to think how to get the charge ##q## from this. Since the balls are stationary the force felt on each of the balls must equal the force of gravity on the balls:
The force of gravity on the balls is ##mg \sin \frac{\theta}{2} ##.
However, if I set ##F## equal to this I do not get the answer in the book. The answer in the book is
$$\sqrt{(mg) \tan \frac{\theta}{2}4\pi \epsilon_0 4 L^2 \sin^2 \frac{\theta}{2}}$$
This,to me, suggests that the force on the ball is given by ##(mg) \tan \frac{\theta}{2}##. Could someone explain to me why this is the case?