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A positive charge q is fixed at the point x=0,y=0 and a negative charge -2q is fixed at the point x=a,y=0.

Part A:
Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the charges.

Part B:
At which positions on the y-axis is V = 0?

Part C:
What does the answer to part A become when y>>a?

Part D:
Explain why this result is obtained.
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A positive charge 'q' is fixed at the point x= 0, y= 0, and a negative charge '-2q' is fixed at the point x=a , y = 0.

a) The electric potential V is a scalar
Suppose P is a point at distance y from +q on the x axis
The electric potential at distance x from+q =V1= kq / y
The electric potential at distance (y-a) from - 2q =V2= -2kq / (y - a)
Total electric potential =V1 + V2
Total electric potential = kq / y -2kq / (y - a)
Total electric potential =kq { (1 / y) - [2 / (y - a)] }
Total electric potential =kq ( y -a -2y) / y (y - a
Total electric potential =kq ( y + a) / x (a - y)
= (1/4pi eo)[1/y -2/(y-a)

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b) V = 0 at positions y/a = -1,0.333 , on the -axis
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c)when y >>a the answer to part A becomes V = -ky /a
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At large 'y' , the potential due to -2q is nearly twice the potential due to +q , hence resultant potential is due to sum of - 2q and +q which is - q

Potential at 'y' = - ky/a
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