Above is shown a \"Tandem Van de Graaff\" accelerator, made of twolarge charged

Question

Above is shown a "Tandem Van de Graaff" accelerator, made of twolarge charged spheres. These types of machines were once used toaccelerate charged particles for experiments.

The two spheres are oppositely charged, one +Q the other -Q, buthave the same radius R. The distance between the centers of thespheres is d.

Which of the following expressions will give the correct valuefor the electrostatic potential at the point "a", very close to thesurface of the positively charged sphere?

(k Q / R) - (k Q / (d -2R)) 2 k Q / (d/2) k Q / R (k Q / (d - R)) - (k Q / (d +R)) 2 k Q / R (k Q / R) + (k Q / (d -2R)) (k Q / R) - (k Q / (d -R)) 2 k Q /(d - R) (k Q / R) + (kQ/d) 2 k Q / d (k Q / R) - (k Q /d) (k Q / R) + (k Q / (d -R)) 2 k Q / (d - 2R)

Explanation / Answer

This is the sum of the potentials from the two spheres. Thecenter of the left sphere is distance R from point A, whilethe center of the right sphere is distance   d -R   from point A.

(k Q / R) - (k Q / (d -2R)) 2 k Q / (d/2) k Q / R (k Q / (d - R)) - (k Q / (d +R)) 2 k Q / R (k Q / R) + (k Q / (d -2R)) (k Q / R) - (k Q / (d -R)) 2 k Q /(d - R) (k Q / R) + (k Q/d) 2 k Q / d (k Q / R) - (k Q / d) (k Q / R) + (k Q / (d -R)) 2 k Q / (d - 2 R)

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