1. if the charges q=e and -2q=-2e are separated by a distance d=1 micron, find t

Question

1. if the charges q=e and -2q=-2e are separated by a distance d=1 micron, find the potential at a point a distance x on the x-axis.
2. using the formula E= - dV/DX x, find the electric field due to the quadrupole.
3. if a uniform electric field of strength 100 N/C is incident from left to right along the x axis, what is the force on the q charges if the -2q charge is a pivot point.
4. find the torque on the two charges. what does the quadrupole do in response to the field?

Explanation / Answer

As you asked multiple questions, so l am bound to answer first one.

(1)

Potential at distance x,

V = k*e / r + k(-2e) / x + ke / r

r = sqrt (d^2 + x^2)

r = sqrt [(10^(-6))^2 + x^2] = sqrt ((10^(-12) + x^2)

V = ke /  sqrt ((10^(-12) + x^2) - ke / x + ke /  sqrt ((10^(-12) + x^2)

V = 2ke (1 / sqrt ((10^(-12) + x^2) - 1 / x)

since, 10^(-12) is very small so, we can write it

V = 2ke (1 / x - 1/ x)

V = 0

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