# 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

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