Example 25.4 The Electric Potential of a Dipole Problem An electric dipole consi

Question

Example 25.4 The Electric Potential of a Dipole Problem An electric dipole consists of two charges of opposite sign but equal magnitude separated by a distance 2a as in Figure 25.14. The dipole is along the x axis and is centered at the origin. el el Calculate the electric potential at any point P along the axis Calculate the electric field on the axis at points very far from the dipole. Calculate V and Ex if point P is located anywhere between two charges . -q E Figure 25.14 An electric dipole located on the x axis. Strategy Use Equations 25.12 and 25.16.

Explanation / Answer

Electric potential is given by - k*q/r

Two Charges are - +q @ 0 & -2q @ 2.10

Let the Electric Potential be zero at distance x m from charge +q towards +ve Xaxis.
Distance from charge -2q = (2.1 - x) m

Electric Potential = k * q/x - k*2q/(2.1 -x)
0 =  k * q/x - k*2q/(2.1 -x)
k * q/x = k*2q/(2.1 -x)
1/x = 2/(2.1 - x)
2.1 - x = 2x
3x = 2.1
x = 2.1/3
x = 0.7 m

Let the Electric Potential be zero at distance x m from charge +q towards - ve Xaxis.
Distance from charge -2q = (2.1 + x) m

Electric Potential = k * q/x - k*2q/(2.1 + x)
0 =  k * q/x - k*2q/(2.1 + x)
k * q/x = k*2q/(2.1 + x)
1/x = 2/(2.1 + x)
2.1 + x = 2x
x = 2.1

This lies in -ve Xaxis , Therefore x = -2.1 m

Electric Potential is zero at :-

Smaller Value = -2.1m
Larger Value = 0.7 m

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