Question

Question 6 (5 marks) Two non-conducting spheres of equal radii R are placed adjacent to each other as shown in figure 5. Sphere 1 has a charge +91 distributed uniformly throughout its volume, and sphere 2 has charge +92 distributed uniformly throughout. A point P is chosen on the line joining the centers of the two spheres, at a distance R/2 from the centre of sphere 1 and 3R/2 from the centre of sphere 2. If the net electric field at the point P is zero, compute the ratio of the two charges 91/92- [Hint: Use Gauss's law to compute the electric field due to the spheres at the point P.] R 2 Figure 5: Two adjacent charged spheres. Question 7 (10 marks) Consider a spherically symmetric charge distribution with a charge per unit volume p(r) given by 4r p(r) = po 1 - 3R = 0 for r >R ( for TSR Here po is a positive constant. 1. What is the total charge carried by the distribution? (1 mark) 2. Find the electric field magnitude at a point P when it is at a radial location r > R. (2 marks) 3. Find the electric field magnitude at a point P when it is at a radial location r < R. (3 marks) 4. Sketch a plot depicting the electric field magnitude E(r) as a function of r for 0 STSR. (2 marks) 5. Find the value of r at which E(r) is a maximum. What is the value of E(r) at this point? (1+1 marks) [Hint: A thin spherical shell of inner radius r and outer radius r + dr has a volume equal to 4rr dr. Thus the charge carried by this thin shell is p(r) x 4mrdr.]

Answer 1

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