Two tiny spheres carrying charges 1.5 μC and 2.5 μC are located 30 cm apart. Find the potential and electric field:
(a) at the mid-point of the line joining the two charges, and
(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.
Potential at any point is given by, V = 
N m C-1
Electric field generated by a charge, E = 
N C-1
Where,
q = charge
d = distance from origin
ϵ0 = permittivity of space
and, 
= 9 × 109 N m2 C-2
(a) Figure below represents the given situation,
Let the potential at O (midpoint) be V and Electric field be E.
We have,
∴ V = 
+ 
= 2.4 × 105 N m C-1
and,
E = electric field due to charge 2.5μC – electric field due to charge 1.5μC
∴E = 
⇒ E = 4 × 105 N C-1
(b) Figure below represents the given situation,
From the figure point Z is required location and its distance from both the charges is equal and equal to,
d = AZ = BZ = 
⇒ d = 0.18 m
and θ = 
∴ θ = 56.250
Thus, Potential and electric field at point Z is given by,
V = 
⇒ V = 2 × 105 N m C-1
and,
E = 
Where,
E1 = electric field generated by 1.5μC charge at Z
E2 = electric field generated by 2.5μC charge at Z
and, θ = angle between distance and perpendicular height (as shown above) and,
∴ E = 6.6 × 105 N C-1