Question

Consider two charged objects lying along the x-axis. A 2.0 x 10-9 C point charge is located at x = 3.0 cm and a -3.0 x 10-9 C point charge is located at x = 5.0 cm.

a) What is the magnitude of the force on the negatively charged object due to the positively charged object? What is its direction? Show your work and explain your reasoning.

b) Suppose the -3.0 x 10-9 C charge is moved to x = 5.0 cm and y = 6.0 cm. What is the magnitude of the force exerted by the negative point charge on the positive point charge? What is its direction? Show your work and explain your reasoning.

Answer 1

a)

$$F=\frac{kq_1q_1}{r^2}\\F=\frac{(9\cdot10^{9})(2\cdot10^{-9})(3\cdot10^{-9})}{(0.05-0.03)^2}=0.000135\ N$$

The force directed from negatively charged object to the positively charged object (negative x-direction).

b)

$$F=\frac{(9\cdot10^{9})(2\cdot10^{-9})(3\cdot10^{-9})}{0.03^2+0.06^2}=0.000012\ N$$

The direction:

$$\theta=\arctan{\frac{6}{5}}=50\degree$$

counterclockwise from negative x-direction (from negatively charged object to the positively charged object).