A sphere of radius 2a is made of a non-conducting material that has a uniform volume charge density 1. (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the sphere, as shown in Figure P24.64. Show that the electric field within the cavity is uniform and is given by Ex = 0 and Ey = ρa/3?0.
A sphere of radius 2a is made of a non-conducting material that has a uniform volume charge density 1. (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the sphere, as shown in Figure P24.64. Show that the electric field within the cavity is uniform and is given by Ex = 0 and Ey = ρa/3?0.
Scenario - A cavity is cut out from a sphere, that is made from a non conducting material that has certain volume charge density.
Given :
Radius of sphere
Radius of cavity
Positive charge density gives a positive electric field while absence of positive charge density implies a negative charge density gives negative electric field. Net electric field is a combination of these two.
Area and volume of sphere are:
Then from Gauss's Law :
Electric field because of sphere
along Y direction.
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