1. 16.2 Electric potential around a point charge
At any point around a point
charge, the electric potential
is given by:
where
According to the above formula, the electric potential at
infinity (r = ) is zero. q r
V = ?
q: the point charge (C)
r: the distance between
the charge and the
point (m)

2. Remarks about Electric potential around a point charge
Signs are counted in calculations.
Electric potential around a positive charge is positive and around a negative charge is negative.
Electric potential around a point charge is inversely proportional to the distance.

3. Remarks about Electric potential around a point charge
All the previous formulae of electric potential and electric potential difference could be applied when ever needed
∆V = Vf – Vi
W = - ∆PE
W = - ∆V q

4. Examples on electric potential around a point charge
Determine the electric potential at a point, 2 m from a point charge of -10 C?
Answer:
Given:
q = -10 C = -10 x 10-6 C
r = 2 m

5. Examples on electric potential around a point charge
How much work is needed to move a charge of -5 nC from infinity to a point which is 200 mm from a positive point charge of 6 C.
Answer:
Given:
qo = -5 nC = -5 x 10-9 C
q = 6 C = 6 x 10-6 C
r = 200 mm = 200 x 10-3 m
W = -qo ∆V
=- (-5 x 10-9 (Vf – Vi))
(Vi = 0 at infinity, Vf
is at point)
W = `5 x 10-9 (2.7 X 105 – 0)
= x 10-3 J

6. Electric potential at a point with multiple point charges around itq1 q2 q3 r1 r2 r3
Vtotal = ?
To find the electric potential
at a point with multiple point
charges around it:
- We find the electric potential at the point
for each charge individually.
- we add the individual electric potential
algebraically (take signs in account).
Vtotal = V V2 + V3 + ………..

7. Examples on electric potential around a point charge
The two charges in the opposite
Figure are separated by a distance
of 2 cm. Calculate the total electric
potential at point B which is the
midpoint between the two charges.
Answer:
At point B there are two electric potentials due to the two
charges. So
Vtotal = V V2
Vtotal =
Vtotal =
Vtotal = V