# A positive point charge in front of a grounded conducting metal plate.docx

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A positive point charge in front of a grounded conducting metal plate induces negative charges on the metal plate. Consider a point P on the metal surface at the distance from the point directly beneath the positive point charge with a charge . The electric field at P is normal to the surface and is directed into it. By using the negative image charge, show that the magnitude of the electric field at P is The induced charge density at any point on the metal surface is By integrating over the whole surface, show that the total induced charge is . There is mutual attraction between the positive point charge and the induced negative surface charges. By using the negative image charge, calculate the magnitude of the force that the positive point charge feels toward the metal plate. The induced charge at the metal surface for an element of area feels a force whose direction is surface-normal and whose magnitude is , where is the areal density of the induced charge and is the magnitude of
• Fall '19
• Electric charge, metal plate, positive point charge, metal surface

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