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**Potential due to an Electric Dipole**

The 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 r_{1} and r_{2} 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

cosÎ¸=OC/OP = OC/a

therefore OC=acosÎ¸ similarly OD=acosÎ¸

Now ,

r_{1} = QRâ‰…RD = OR-OD = r-acosÎ¸

r_{2} = PRâ‰…RC = OR+OC = r+acosÎ¸

since magnitude of dipole is

|**p**| = 2qa

If we consider the case where r>>a then

again since pcosÎ¸= **pÂ·rË†** where,** rË†** 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 r^{2} not ad 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**.**Potential Due To A System Of Charges**

Consider a system of charges q_{1}, q_{2},â€¦, qn with position vectors r_{1}, r_{2},â€¦, r _{n} relative to some origin. The potential V_{1} at P due to the charge q_{1} is

where r_{1P} is the distance between q_{1 } and _{P}. Similarly, the potential V_{2} at P due to q_{2} and due to q are given by

where r_{2P} and r_{3P} are the distances of P from charges q_{2 }and q_{3}, respectively; and so on for the potential due to other charges.

By the superposition principle, the potential V at P due to the total charge configuration is the algebraic sum of the potentials due to the individual charges

The electric field outside the shell is as if the**entire charge is concentrated at the centre**. Thus, the potential outside the shell is given by

where q is the total charge on the shell and R its radius. The electric field inside the shell is zero. This implies that potential is constant inside the shell (as**no work is done in moving a charge inside the shell**), and, therefore, equals its value at the surface, which is

The electric field outside the shell is as if the

where q is the total charge on the shell and R its radius. The electric field inside the shell is zero. This implies that potential is constant inside the shell (as

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