Electric Field at Surface of Earthed Sphere (using image charges)

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SUMMARY

The discussion focuses on calculating the electric field at the surface of an earthed conducting sphere influenced by an external charged sphere. The image charge method is employed, with the image charge defined as q' = -(aq/d) and positioned at a distance b = (a^2)/d from the center of the sphere. It is concluded that while the electric potential is zero on the surface of the sphere, the electric field is non-zero due to the gradient of the potential, which is not uniform across the space surrounding the sphere.

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  • Basic calculus for understanding gradients
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"A charged sphere is a distance d from the centre of an earthed sphere conducting sphere of radius a. An image charge (q') for this system is located at a distance b from the centre of the sphere where:

q'= -(aq/d) and b=(a^2)/d

Calculate the expression for the Electric field at point p being on the surface of the sphere directly above the surface."

Would the Electric field be zero. As the Electric potential would surely be zero on the surface of the sphere and the E field is just -grad of the potential?
 
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The potential is zero on the surface (and in the interior), but non-zero everywhere else. This gives a non-zero electric field.
In a similar way, you can define the floor as area of zero gravitational potential - and still get a gravitational field.
 

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