Why must electrostatic field be normal to the surface at every point of a charged conductor?

Question

Answer

Because surface of a conductor is an equipotential surface , in which component of electric field along the surface of conductor is zero , so only component of electric field which is perpendicular to its surface exists.

Answer

As there is no potential gradient along the surface of conductor hence there would be no electric field along the surface..

=> electric field must be normal to surface...

Answer

Introduction:
The electrostatic field refers to the region around a charged object where the electric forces act. For a charged conductor, the electrostatic field must be normal (perpendicular) to the surface at every point. This fundamental principle can be explained in detail.

1. Electrostatic equilibrium:
A charged conductor is in a state of electrostatic equilibrium when the net electric field inside it is zero. This means that the charges on the conductor have come to a stable distribution and there is no movement of charge within the conductor.

2. Electric field inside a conductor:
Inside a conductor, the electric field is zero. This is because any electric field present inside the conductor would cause the free charges within the conductor to move until they reach a state of equilibrium, neutralizing the field.

3. Electric field at the surface:
At the surface of a charged conductor, the electric field must be non-zero. This is because the charges on the surface of the conductor repel each other and create an electric field.

4. Normal to the surface:
The electric field at the surface of a charged conductor must be normal to the surface at every point. This is due to the following reasons:

4.1 Surface charge distribution:
The charges on the surface of a conductor distribute themselves in such a way that the electric field lines are normal to the surface. This ensures that the charges do not experience any tangential forces, which would cause them to move along the surface.

4.2 Electrostatic shielding:
The normal electric field at the surface of a conductor plays a crucial role in electrostatic shielding. When an external electric field is applied to a conductor, the charges on the surface rearrange in such a way that the electric field inside the conductor is zero. This shielding effect is only possible if the electric field is normal to the surface, as any tangential component would not be canceled out.

Conclusion:
In conclusion, the electrostatic field must be normal to the surface at every point of a charged conductor due to the principles of electrostatic equilibrium, the absence of electric field inside the conductor, and the requirements of surface charge distribution and electrostatic shielding. This ensures stability, zero net electric field inside the conductor, and effective protection against external electric fields.

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