Question

Electric
potential energy possessed by a charge
q placed at
the equatorial position of
electric dipole (P = 2qa) at a
from
rom the centre of the
distance
r
dipole is​

Answer 1

Answer:

We already know that electric dipole is an arrangement which consists of two equal and opposite charges +q and -q separated by a small distance 2a.

Electric dipole moment is represented by a vector p of magnitude 2qa and this vector points in direction from -q to +q.

To find electric potential due to a dipole consider charge -q is placed at point P and charge +q is placed at point Q as shown below in the figure.

Potential due to an electric dipole

Since electric potential obeys superposition principle so potential due to electric dipole as a whole would be sum of potential due to both the charges +q and -q. Thus

where r1 and r2 respectively are distance of charge +q and -q from point R.

Now draw line PC perpandicular to RO and line QD perpandicular to RO as shown in figure. From triangle POC

cosθ=OC/OP = OC/a

therefore OC=acosθ similarly OD=acosθ

Now ,

r1 = QR≅RD = OR-OD = r-acosθ

r2 = PR≅RC = OR+OC = r+acosθ

since magnitude of dipole is

|p| = 2qa

If we consider the case where r>>a then

again since pcosθ= p·rˆ where, rˆ is the unit vector along the vector OR then electric potential of dipole is

for r>>a

From above equation we can see that potential due to electric dipole is inversly proportional to r2 not 1/r which is the case for potential due to single charge.

Potential due to electric dipole does not only depends on r but also depends on angle between position vector r and dipole moment p.