What is the work done in moving a point charge and electric field is always at right angles to equipotential surface?
Yes, the work done in moving a point charge by an electric field is always at right angles to the equipotential surface. This is a fundamental principle in electromagnetism and has several important implications.
Here's why:
Therefore, the electric field lines must be perpendicular to the equipotential surface at all points. This ensures that moving a charge along the surface doesn't involve any work against the electric field.
This principle has various applications in electrostatics and electrodynamics, including:
- Calculating potential differences: By knowing the shape of equipotential surfaces and the distance between them, we can determine the potential difference between points.
- Analyzing charge distributions: The direction of electric field lines relative to equipotential surfaces helps visualize and understand how charges are distributed in space.
- Designing electrical circuits: Equipotential surfaces are crucial for designing efficient circuits, ensuring charges flow along paths with minimal potential changes (and therefore minimal energy loss).
Moving a Point Charge in an Electric Field: When a point charge moves inside an electric field, the electrostatic force does work on the charge. Work is the product of force (electrostatic force in this case) times the distance that the point charge has traveled. The work done by a magnetic field on a moving charge is zero since the magnetic force is perpendicular to the velocity. However, magnetic forces in a multiparticle system can rearrange the energy inside the system if these forces do as much negative work as they do positive work, resulting in a net work done of zero. Then move to explain the electric potential and the work is done in an electric field. Then use the equation $W = qV$ to calculate the work done. The electric field is conservative, therefore if we move a charge in the field, opposite to the direction normally the electron moves freely, then we are doing some work and this work is stored as the potential energy. Therefore to move the charge $q$ from one point to another the work done will be $Vq$. The angle between Electric field and an equipotential surface is always 900. This is because, when the potential becomes constant, the negative potential gradient also becomes zero, hence necessitating the need for Electric field to be always normal with surface. Now θ = 90o means that the angle between electric lines of forces or electric field and the equipotential surface is 900. The electric field line shows the direction of the electrostatic force on a charge. Since there's no component of force along an equipotential line, field lines must intersect them at right angles.Electric field is defined to be the gradient of potential and the surface of a conductor has a constant potential. Therefore, there is no field along the surface of the conductor and hence, the elctrostatic field at the surface of a charged conductor should be normal to the surface at every point.