Work and the Magnetic Field

There are two main reasons why no work is done when a charge moves perpendicular to a magnetic field:

Think of it like this: the magnetic field just gives the charged particle a sideways nudge, constantly changing its direction but not affecting its speed. It's like guiding a ball on a circular track - you're not pushing it forward, just keeping it on the path.

Equipotential Surfaces and Intersections

Equipotential surfaces are like invisible level surfaces in an electric or magnetic field where the potential (voltage or magnetic scalar potential) is the same at every point. They're like contour lines on a map, showing regions of equal "height" in the field.

Now, imagine two such surfaces trying to intersect. If they did, it would mean the potential at that point would be the same for both surfaces, violating the very definition of equipotential. It's like trying to have two different water levels at the same point in a pond - it just doesn't work.

So, equipotential surfaces never intersect because they represent distinct levels of potential, and having the same potential at multiple points would contradict their fundamental nature.

Here's an analogy: imagine two floors in a building. Each floor represents an equipotential surface. People can walk around on each floor, but they can't be in two places at once, right? Similarly, the potential can't be "on" two different surfaces simultaneously.

Dr Murtadha Shukur thank you for your contribution to the discussion

Work is done on a charge when it moves against an electric field. On an equipotential surface, the electric potential is constant everywhere, meaning there's no potential difference between any two points. As there's no potential difference, no work is required to move a charge from one point to another on the surface.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. Another way to look at this is that the magnetic force is always perpendicular to velocity, so that it does not work on the charged particle. The particle's kinetic energy and speed thus remain constant. The direction of motion is affected but not the speed. The velocity component perpendicular to the magnetic field creates circular motion, whereas the component of the velocity parallel to the field moves the particle along a straight line. When a charged particle moves perpendicular to the uniform magnetic field, the magnetic force will act perpendicular to the velocity at every instant which makes the particle move in a circular path with constant velocity v. Thus, the magnitude of velocity remains same, but the direction changes. An charged particle moving perpendicular to an external uniform magnetic field moves in a circular orbit whose centripetal acceleration is provided by tg magnetic force, that is, mv2r=qvB. An electron beam passes through a region of crossed electric and magnetic fields of strength E and B respectively. They can't intersect each other because two different equipotential surfaces have different electric potential, so if they intersect then the point of intersection will have two different potential at the same point which is not possible. Two equipotential surfaces cannot intersect each other because two different equipotential surfaces have different electric potentials, so if they intersect then the point of intersection will have two different potentials at the same point which is not possible. Equipotential lines at different potentials can never cross either. This is because they are, by definition, a line of constant potential. The equipotential at a given point in space can only have a single value.