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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