(a) "The outward electric flux due to charge +Q is independent of the shape and size of the surface which encloses is." Give two reasons to justify this statement. (b) Two identical circular loops '1' and '2' of radius R each have linear charge densities −λ and +λ C/m respectively. The loops are placed coaxially with their centres R3 distance apart. Find the magnitude and direction of the net electric field at the centre of loop '1'.



In electromagnetism, electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. If the electric field is uniform, the electric flux passing through a surface of vector area S is \Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta, where E is the electric field (having units of V/m), E is its magnitude, S is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to S. For a non-uniform electric field, the electric flux dΦE through a small surface area dS is given by d\Phi_E = \mathbf{E} \cdot d\mathbf{S} (the electric field, E, multiplied by the component of area parallel to the field). The electric flux over a surface S is therefore given by the surface integral: \Phi_E = \iint_S \mathbf{E} \cdot d\mathbf{S} where E is the electric field and dS is a differential area on the closed surface S with an outward facing surface normal defining its direction.