Electric Field Intensity (E) Due To a Circular Ring Charge - Field Theory.
- Consider a circular ring of radius 'a' which carries a uniform line charge density ρ L as shown in figure. - We need to find out electric field at a point P (0, 0, h) on the z axis (z > 0). - Electric field intensity (E) due to any line charge (ρ L ) in general is given as: In this case, dl = a dφ (Since the differential part dl is a differential arc ) R 2 = a 2 + h 2 Consider the triangle shown in the above figure a a ρ + R = h a z → R = - a a ρ + h a z a R = R / | R | a R = - a a ρ + h a z / ( a 2 + h 2 ) 1/2 Substituting all these values in the above equations, the electric field intensity E becomes: - For every element dl there is a corresponding element diametrically opposite that gives an equal but opposite dE ρ so that the two contributions cancel each other. Hence contribution along a ρ due to symmetry adds up to zero. - Therefore the final electric field intensity at point (0, 0, h) has ...