Question

A small sphere with mass 1.50 g hangs by a thread between two very large parallel vertical plates 5.00 cm apart (Fig. P23.59). The plates are insulating and have uniform surface charge densities +$\mathit{\sigma }$and -$\mathit{\sigma }$. The charge on the sphere is$\mathit{q}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathit{C}$. What potential difference between the plates will cause the thread to assume an angle of 30.0° with the vertical?

Short answer

The potential difference between the plates V = 47.75V

Step-by-step solution

Step 1:

Given data:

Potential of two infinite parallel plates;

V=Ed

Electric filled is

From the above two equation

Step 2:

As the ball is in equilibrium therefore the net force acting on the ball is zero.

So, the vertical component of tension will equalize the weight and the horizontal component will equalize electric force.

From the above equation;

Putting the value of $F_e$in equation

Hence, the potential difference between the plates V = 47.75 V.