A dipole is oriented along the axis. The dipole moment is (Assume the center of the dipole is located at the origin with positive charge to the right and negative charge to the left.) (a) Calculate exactly the potential (relative to infinity) at a location < , 0, 0 > on the axis and at a location < 0, , 0 > on the axis, by superposition of the individual contributions to the potential. (Use the following as necessary: q, ε0, x, s and y.)

The potential that is as a result of the dipole at <x,0,0> is

The potential that is as a result the dipole at <0,y,0> is  

Explanation:

From the question we are told that

    The dipole moment is  

The potential at the position <x,0,0 > on the x-axis is mathematically represented as

So this can be evaluated as

where s is the distance between the charges

   =>  

The potential at the position <0,y,0 > on the y-axis is mathematically represented as

So this can be evaluated as

The negative sign shows that the potential value right side of the minus sign is a negative potential

Note

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west