A simple pendulum has a mass m and carries a charge q. The pendulum is suspended between the
vertical plates of a capacitor of separation distance d. If the string of the pendulum makes an angle
θ with the vertical, what is the potential difference between the plates
To find the potential difference between the plates of the capacitor, we need to consider the electrostatic force acting on the charged pendulum due to the electric field between the plates.
Step 1: Calculate the electric field between the plates
The electric field between the plates of a capacitor is given by the equation E = V/d, where E is the electric field magnitude, V is the potential difference between the plates, and d is the separation distance between the plates. Rearranging the equation, we have V = E * d.
Step 2: Determine the force on the charged pendulum
The force acting on the charged pendulum due to the electric field is given by the equation F = q * E, where F is the force, q is the charge on the pendulum, and E is the electric field magnitude.
Step 3: Find the tangential component of the force
The tangential component of the force is given by F_t = F * cos(θ), where F_t is the tangential force and θ is the angle the string makes with the vertical.
Step 4: Calculate the potential difference between the plates
Now, we can calculate the potential difference between the plates using the tangential force as follows:
V = (F_t * L) / q, where L is the length of the pendulum string.
By substituting the equations and given values, we can find the potential difference between the plates for a given angle θ.