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Find the electric field at the center of the sphere due to the induced charges on the surface of the sphere, as shown in Fig. 22-30. |
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Answer» Solution :KEY IDEA Here, we note that the induced charges will form a certain pattern on the surface of the sphere which cannot be predicted. But we can find the electric field due to q at any point. The NET electric field inside the conductoris zero. This is produced by the induced charged and the external charge. Calculations: At the CENTER this electric field due to q in the positive direction will be (Fig. 22-31): `E_(Q)=(q)/(4pi epsilon_(0)d^(2))`.  Since the net electric field at the center has to be zero. `E_("induced")+E_(Q)=0 RARR E_("induced")= -(q)/(4pi epsilon_(0)d^(2))`. Here, the charges will be induced on the surface of the sphere, but they will not be uniformly distributed. So, we cannot apply the formula for the electric field due to a uniformly charged spherical SHELL. Learn: When we say the electric field is zero, this implies that electric field should be zero inside the core of a solid metal. These are the points where the free electrons are present within the LATTICE. These free electrons should not experience any force. |
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