Figure a shows a solid metallic sphere of radius R =12 cm which is charged with

Question

Figure a shows a solid metallic sphere of radius R =12 cm which is charged with q = 1.6 mu C. Assume the potential of the electric field to be zero at infinity. Find the potential VR on the surface of the sphere SR. On Fig. a, draw the cross-section of an equipotential surface Sp at a distance r = 20 cm from the center of the sphere. What is the value of the potential Vr on the surface Sp? An electron is moved along Path-I (shown as a dashed line in Fig. a) from point B on the surface SR to the point P on the surface Sp. How much work W is done by the electrostatic force? How much energy U is required to move an electron from a point on the surface SR to the point on the opposite side of the surface of the sphere? Justify your answer. Now, four such charged spheres are used to form a configuration of a square with side a = 1.6 m as shown in Fig. b. Find the potential VA at point A.

Explanation / Answer

(3)

(a)

The potential VR on the surface of the sphere is given by

VR =Kq/R =9*109*1.6*10-6/0.12 =120*103V =120kV

(b) When point lies ouside the sphere then the potenial difference is gvien by

Vo =Kq/r =9*109*1.6*10-6/0.2=72kV

(f)

Given that

Four +q charges are placed at each corner of the sqaure

The distance between the each square is a then distance becomes a/Sqrt(2)

Now potential at the center of the square(VA) is given by

VA=K[q/(a/sqrt(2)+q/(a/sqrt(2)+q/(a/sqrt(2)+q/(a/sqrt(2)]

=4KSqrt(2)q/a =4*9*109*1.414*1.6*10-19/1.6 =81.446*10-10/1.6=50.904*10-10V=5.09*10-9V=5.09nV

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