Prove that the field on the surface of a sphere carrying a uniformly distributed electric charge is equal to that which would have been established, if the entire charge were concentrated in the centre of the sphere.

Prove that the field on the surface of a sphere carrying a uniformly d

1.	Prove that the field on the surface of a sphere carrying a uniformly distributed electric charge is equal to that which would have been established, if the entire charge were concentrated in the centre of the sphere.
Answer» <html><body><p></p>Solution :Construct a second sphere <a href="https://interviewquestions.tuteehub.com/tag/around-5602275" style="font-weight:bold;" target="_blank" title="Click to know more about AROUND">AROUND</a> the sphere under consideration and suppose it carries a charge <a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> in magnitude, but opposite in sign (Fig. 24.14). According to the result <a href="https://interviewquestions.tuteehub.com/tag/obtained-7273275" style="font-weight:bold;" target="_blank" title="Click to know more about OBTAINED">OBTAINED</a> in the <a href="https://interviewquestions.tuteehub.com/tag/previous-592857" style="font-weight:bold;" target="_blank" title="Click to know more about PREVIOUS">PREVIOUS</a> problem, the charge of the outer sphere does not create a field inside it. Therefore the field between the spheres is created only by the charge of the internal sphere. If there is <a href="https://interviewquestions.tuteehub.com/tag/little-1075899" style="font-weight:bold;" target="_blank" title="Click to know more about LITTLE">LITTLE</a> difference between the radii of these spheres (i.c. if `R_(1)-R lt lt R)` , the field in between will be almost homogeneous, and its strength will be (see 37.5) <br/> `E=(sigma)/(epsi_(0))=(Q)/(epsi_(0)S)=(Q)/(4pi epsi_(0)R^(2))`</body></html>

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Prove that the field on the surface of a sphere carrying a uniformly distributed electric charge is equal to that which would have been established, if the entire charge were concentrated in the centre of the sphere.

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