We have discussed the potential due to point charge, electric dipole, etc. Now let us go through the equipotential surface and its properties.
An equipotential surface is a surface with a constant value of potential at all points on the surface.
Properties of Equipotential Surface
This shows that V is a constant if r is constant. Thus, equipotential surfaces of a point charge are concentric spherical surfaces centred at the charge. Now the electric field lines for a single charge q are radical lines starting from or ending at the charge, depending on whether q is positive or negative. Clearly, the electric field at every point is normal to the equipotential surface passing through that point. Theis is true in general: for any charge configuration, electric field at any point is normal to the electric field at that point. Why should it be normal?
If the field were not normal to the equipotential surface, it would have non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have to be done. But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface. The electric field must, therefore, be normal to the equipotential surface at every point.
Equipotential surfaces offer an alternative visual picture in addition to the picture of electric field lines around a charge configuration. For a uniform electric field E, say, along the x- axis, the equipotential surfaces are planes normal to the x-axis, ie, planes parallel to the y-z plane.
An equipotential surface is a surface with a constant value of potential at all points on the surface.
Properties of Equipotential Surface
This shows that V is a constant if r is constant. Thus, equipotential surfaces of a point charge are concentric spherical surfaces centred at the charge. Now the electric field lines for a single charge q are radical lines starting from or ending at the charge, depending on whether q is positive or negative. Clearly, the electric field at every point is normal to the equipotential surface passing through that point. Theis is true in general: for any charge configuration, electric field at any point is normal to the electric field at that point. Why should it be normal?
If the field were not normal to the equipotential surface, it would have non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have to be done. But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface. The electric field must, therefore, be normal to the equipotential surface at every point.
Equipotential surfaces offer an alternative visual picture in addition to the picture of electric field lines around a charge configuration. For a uniform electric field E, say, along the x- axis, the equipotential surfaces are planes normal to the x-axis, ie, planes parallel to the y-z plane.
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