There are two parallel conductive plates separated by a distance d and zero potential. calculate the potential and electric field that occurs if a q charge is placed between the plates at a distance d/2.

The total electric potential at mid way due to 'q' is

The net Electric field at midway due to 'q' is 0.

Solution:

According to the question, the separation between two parallel plates, plate A and plate B (say)  = d

The electric potential at a distance d due to 'Q' is:

Now, for the Electric potential for the two plates A and B at midway between the plates due to 'q':

For plate A,

Similar is the case with plate B:

Since the electric potential is a scalar quantity, the net or total potential is given as the sum of the potential for the two plates:

Now,

The Electric field due to charge Q at a distance is given by:

Now, if the charge q is mid way between the field, then distance is .

Electric Field at plate A, at midway due to charge q:

Similarly, for plate B:

Both the fields for plate A and B are due to charge 'q' and as such will be equal in magnitude with direction of fields opposite to each other and hence cancels out making net Electric field zero.

the device is called “ rocket engine”

the electric field is a “force field” around a charged object that illustrates the direction the electric force would push an imaginary