Suppose the conducting spherical shell in the figure below carries a charge of 2

Question

Suppose the conducting spherical shell in the figure below carries a charge of 2.60 nC and that a charge of -2.40 nC is at the center of the sphere. If a = 1.60 m and b = 2.30 m, find the electric field at the following. (a) r=1.50m magnitude 9.59 N/C direction radially inward (b) r=2.20m magnitude 0 N/C direction The magnitude is zero. (c) r=2.50m magnitude 1.44 direction radially outward Your response differs from the correct answer by more than 100%. N/C radially outward (d) What is the charge distribution on the sphere? inner surface nC outer surface nC

Explanation / Answer

(3) For r =   2.5   m    here r > b   

The point lies outside the shell

Let us constuct a gaussian surface with radius r >b

Electric field E =   qenl /   40 r2     

Here qenl    =    charge on the shell   + charge at the centre     =   2.6 nC - 2.4nC = 0.2*10^-9 C

E =   0.2*10^-9 C /   40 (2.5 m)^2

E   =   0.288N/C

(d) charge at the centre of the shell induces an equal and opposite charge on the inner surface of the shell

charge induced on the inner surface of the shell    Qinner    = 2.4 nC

Charge on the outer surface Qouter    =   2.6 nC - 2.4 nC =   0.2 nC

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