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 = 1a/3/0. (Suggestion: The field within the cavity is the superposition of the field due to the original uncut sphere, plus the field due to a sphere the size of the cavity with a uniform negative charge density -1.)

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