Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at...

Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at (1,0). Calculate the electric potential everywhere in the plane.

Expert Solution

Potential due to an electric dipole

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.
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
cos?=OC/OP = OC/a
therefore OC=acos? similarly OD=acos?
Now ,
r₁ = QR?RD = OR-OD = r-acos?
r₂ = PR?RC = OR+OC = r+acos?

since magnitude of dipole is
|p| = 2qa
If we consider the case where r>>a then

again since pcos?= p

genius_generous answered 9 months ago

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