Consider a grounded conducting sphere of radius R. A very small object with charge Qis brought...

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Consider a grounded conducting sphere of radius R. A very small object with charge Qis brought in to a distance a from the surface of the sphere. The electric field lines can be found by replacing the sphere with a single image charge Q' along the axis between Q and the center of the sphere so that the field satisfies the same boundary conditions. (a) State the boundary conditions on Ē. (b) Find Q' and its distance from the center of the sphere and its distance from the center of the sphere (this can be done using dimensional arguments if you so desire). (c) Calculate the force on the sphere from the charge Q. Optional: (d) Consider a conducting sphere with a cubical cavity inside, centered on the sphere. A very small conductor with electric charge Q is suspended inside the cavity on a diagonal of the cube halfway between the center of the cube and one corner. Find the field outside the sphere. Please explain each step in your calculation (it may help in clarity to number each step). Go to Settings to activate Windows. Consider a grounded conducting sphere of radius R. A very small object with charge Qis brought in to a distance a from the surface of the sphere. The electric field lines can be found by replacing the sphere with a single image charge Q' along the axis between Q and the center of the sphere so that the field satisfies the same boundary conditions. (a) State the boundary conditions on Ē. (b) Find Q' and its distance from the center of the sphere and its distance from the center of the sphere (this can be done using dimensional arguments if you so desire). (c) Calculate the force on the sphere from the charge Q. Optional: (d) Consider a conducting sphere with a cubical cavity inside, centered on the sphere. A very small conductor with electric charge Q is suspended inside the cavity on a diagonal of the cube halfway between the center of the cube and one corner. Find the field outside the sphere. Please explain each step in your calculation (it may help in clarity to number each step). Go to Settings to activate Windows.

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