Electromagnetic Field Theory
Gradient of scalar field is expressed as

 Outward flux of a vector field per unit volume as the volume about the point tends to zero.
 Maximum rate of increase of scalar function at a point.
 Gradient of divergence of a vector field minus the curl of the vector field.
 Circulation of a vector field per unit area as the area tends to zero.

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Electromagnetic Field Theory
Inside a hollow conducting sphere

 electric field is a non zero constant.
 electric field is zero.
 electric field changes with magnitude of the charge given to the conductor.
 electric field changes with distance from the center of the sphere.

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