Find out the magnitude of electric field intensity of dipole moment P=i^ √3k^ kept at origin at following point (i) 2,0,0 (ii) -1,√3,0?

Question

Answer

Calculation of Electric Field Intensity

Given

Dipole moment, P = i^ √3k^

Electric Field Intensity at Point (2,0,0)

Let the coordinates of point be (x,y,z) = (2,0,0)

Distance from the midpoint of the dipole to point P: r = √(4+0+0) = 2

Electric Field Intensity at point P:

E = (1/4πε) * [(2P/r^3) - P/r^3]

E = (1/4πε) * [(P/r^3)]

E = (1/4πε) * [(i^ √3k^)/(2^3)]

E = (1/4πε) * [(i^ √3k^)/(8)]

E = (1/32πε) * [(i^ √3k^)]

E = (1/32πε) * [√3i^ + k^]

Electric Field Intensity at Point (-1,√3,0)

Let the coordinates of point be (x,y,z) = (-1,√3,0)

Distance from the midpoint of the dipole to point P: r = √(1+3+0) = 2

Electric Field Intensity at point P:

E = (1/4πε) * [(2P/r^3) + P/r^3]

E = (1/4πε) * [(3P/r^3)]

E = (1/4πε) * [(3i^ √3k^)/(2^3)]

E = (1/4πε) * [(3i^ √3k^)/(8)]

E = (3/32πε) * [(i^ √3k^)]

E = (3/32πε) * [√3i^ + k^]