A pair of unlike charges equal in magnitude and separated by a small distance is

Question

A pair of unlike charges equal in magnitude and separated by a small distance is known as a dipole. Such a pair is situated on the x axis at equal distances from the origin as shown in the figure below. The electric field at points to the right of the dipole that are very far compared to the distance between the two charges is given by E =-2kqd/x^3 i cap, where d is the distance between the two charges, k is Coulomb?s constant, and q is the magnitude of the charges of the dipole. (a) What is the potential difference VA-VB, if q = 4.00 nC, d = 2.50 mm, XA = 14.3 cm, and xB = 22.3 cm? V (b) If an electron moves from B to A, what is the change in potential energy of the electron-dipole system? J

Explanation / Answer

Va = Kq/xa - Kq/xa

Va = 9e9 * (4+4) *1e-9* (1/(xa+d) +1/(xa-d)

xa+d = 2.5+1.43 = 3.93 mm

xa- d = 2.5 -1.43 = 1.07 mm

Va = 9e9 *8e-9 /(1/3.93 mm - 1/1.07mm)

Va = 48.96 kV

similarly

Vb   =    9e9 * (4+4) *1e-9/(1/(xb+d) +1/(xb-d)

Vb = 9e9 *8e-9*(1/(xb+d)   - (1/xb-d)

xb + d   = (2.5mm + 2.23mm) = 4.73 mm

xb -d = 2.5 mm - 2.23 mm = 0.27 mm

so

Vb = 9e9 * 8e-9*(1/4.73mm -1/0.27mm)

Vb = 251.44 kV

so Va-Vb = 251.44-48.96   = 202.48 kV

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Pot eenrgy U = Vq

U = 202.48 e 3 * 1.6 e-19

U   = 3.234 *10^-14 Joules

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