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A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potential such that far from the boss the electric field between the plates is Eg. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mf, Ega. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' - -9 1 dVd + a

A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potential such that far from the boss the electric field between the plates is Eg. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mf, Ega. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' - -9 1 dVd + a

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2.10 A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potenti al such that far from the boss the electric field between the plates is Ep. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mé, Ega?. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' = -q 1 dyd + a?
Transcribed Image Text:2.10 A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potenti al such that far from the boss the electric field between the plates is Ep. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mé, Ega?. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' = -q 1 dyd + a?
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