Electrostatics

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Electrostatic

The basic principle of electrostatics is based on the fact the electric charges attract or repel other charges depending on their relative signs and the law of force is given by Coulomb‘s law.

Coulomb’s law states that: The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them. The force is along the straight line joining them.

The electric field E at a point is defined as the electric force F experienced by a positive test charge q placed at that point divided by the magnitude of the test charge.

Properties of Electric Lines of Force or Field Lines

  1. The electric lines of force are imaginary lines.
  2. A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so.
  3. The electric lines of force emanate from a positive charge and terminate on a negative charge.
  4. The tangent to an electric field line at any point gives the direction of the electric field at that point.
  5. Two electric lines of force can never cross each other. If they do, then at the point of intersection, there will be two tangents. It means there are two values of the electric field at that point, which is not possible. Further, electric field being a vector quantity, there can be only one resultant field at the given point, represented by one tangent at the given point for the given line of force.
  6. Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where the electric field is weaker.
  7. Electric lines of force are perpendicular to the surface of a positively or negatively charged body.
  8. Electric lines of force contract lengthwise to represent attraction between two unlike charges.
  9. Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges.

10.The number of lines per unit cross – sectional area perpendicular to the field lines (i.e. density of lines of force) is directly proportional to the magnitude of the intensity of electric field in that region.

  1. Electric lines of force do not pass through a conductor. Hence, the interior of the conductor is free from the influence of the electric field.
  2. Electric lines of force can pass through an insulator.

Gauss’s Law states that The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

Electric field from uniformly charged thin spherical shell:

outside the shell with magnitudeinside the shellwhere:

Q is total charge of the shell

R is radius of the shellis position vector of point P where the electric field is defined

Electric field from uniformly charged solid sphere:outside the sphere with magnitudeinside the sphere with magnitude

Electric field from uniformly charged thin line:

with magnitude where:is linear charge density of the line with length L charged by charge Q

is radius-vector drawn perpendicular to axis of the line from the axis to the point where the electric field is defined

Electric field from uniformly charged thin cylindrical shell:

outside the shell with magnitude

inside the shell

Electric field from uniformly charged solid cylinder:

outside the cylinder with magnitude

inside the cylinder with magnitude

where:

is linear charge density of the cylinder with length L charged by charge Q

R is radius of cylinder

is radius-vector normal to axis of the line drawn from the axis to the point where the electric field is defined

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