Question

A charge of 5C experiences a force of 5000N when it is moved in an electric field. Find the potential difference between the two points separated by a distance of 1cm is
A) 10 V
B) 250 V
C) 1000 V
D) 2500 V

Answer 1

Hint: Use the definition of the electric field and then find the value of the electric field acting on the charge. Then find the value of the potential difference using the definition of the potential difference and the variation in the distance given in the question.

Complete step by step solution:
The concept of the electric field can be explained as below
The electric field is defined as the force acting on the test charge or the unit charge placed in the electric field
The magnitude of the electric field can be obtained using the definition as below
The electric field is E = $ \dfrac{F}{q} $

The value of the electric field acting on the given charge in the question can be calculated as below
The given value of the charge is 5C
The given value of the force acting on the charge is given as 5000N
The value of the field acting on the given charge is obtained as
$E = \dfrac{F}{q} = \dfrac{5000}{5} = 1000 $
So we got the value of the electric field as 1000 volts

Having found the value of the electric field we can now find the value of the potential difference as below using the definition of the potential difference:
The potential difference between two points is defined as the rate of the change of the electric field with respect to the change in the value of the distance from a reference point whose potential is known.

Let us now see the given problem, the value of the distance between the two points is given as 0.01 m
So we get the potential difference using the formula,
$\Delta V = E \times \Delta R$
Where the $\Delta V$ denotes the change in the potential and $\Delta R$ is the change in the value of distance.
So the value of the potential difference becomes $\Delta V = 1000 \times 0.01 = 10 v$

Thus using the definition of the potential difference and the concepts of the electric field we are able to find the value of the potential difference as 10 volts

Note: The concept of the potential difference is defined only when the potential of the reference point is known. The reference point is the one through which we find the value of the potential at any point. So only the potential difference is defined actually and we cannot define the potential at any particular point. This point while understanding the concept has to be considered.