GATE EE 2014 Set 3 — Question 41
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Electromagnetic Fields → Electrostatics → Method of Images
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Question
A perfectly conducting metal plate is placed in - plane in a right handed coordinate system. A charge of columbs is placed at coordinate . is the permittivity of free space. Assume to be unit vectors along , and axes respectively. At the coordinate , the electric field vector (Newtons/Columb) will be
Correct answer
(B) -2 k
Solution
Using the method of images, a point charge at above an infinite grounded conducting plane at induces an image charge at .Given:
Charge at .
Image charge at .
Point of interest .The distance from to is .
The distance from to is also .The electric field at the surface of a conductor is always normal to the surface. Since the plate is in the - plane, the field at will be in the direction.
The magnitude of the electric field at the surface is given by:where is the angle between the line and the normal to the surface (the -axis).Substituting the values:Since the source charge is positive and located above the plate, the electric field at the surface points towards the plate (into the negative direction).
Therefore, .
Charge at .
Image charge at .
Point of interest .The distance from to is .
The distance from to is also .The electric field at the surface of a conductor is always normal to the surface. Since the plate is in the - plane, the field at will be in the direction.
The magnitude of the electric field at the surface is given by:where is the angle between the line and the normal to the surface (the -axis).Substituting the values:Since the source charge is positive and located above the plate, the electric field at the surface points towards the plate (into the negative direction).
Therefore, .
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