Question

An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq.

(a) At a point P, which is far from the dipole (r >> a), show that the electric potential is 

V =Kp cos θ /r²

 

(b) Calculate the radial component E_r and the perpendicular component E_θ of the associated electric field. Note that E_θ = —(1/r) (∂V/∂r). Do these results seem reasonable for

(c) θ = 90° and 0°?

(d) For r= 0?

(e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r= (x² + y²)^1/2  and cosθ =y /(x² + y²)^1/2

and

(f) Using these results and again taking r>> a, calculate the field components; E_x and E_y.