Work done by an electric field

[Stephen2009]

So I was doing an MCAT problem and needed an explanation:

The question involved spoke of the design of an "ink jet printer": a particle is given a NEGATIVE charge and accelerated through 2 parallel plates with an electric field pointing down.

Thus, the electron will be deflected with an upwards trajectory.

Now the first question is "How much work is done by the electric field on the charged particle":

The answer was found using W = (-q)Ed

So my confusion lies in the fact between the work done by the electric field using the comparison of the work done by a magnetic field.

I had an alternate thought no work would have been done since the direction of the electric force exerted by the electric field is perpendicular to the direction of movement of the charged particle.
But obviously my scientific intuition is incorrect b/c I got this question wrong, as work IS done by the electric field.

So where am I going wrong here? How is it that a magnetic field would do no work on this charge and give it a curved trajectory, but when the electric field gives this charged particle a trajectory, it does work in the form of (-q)Ed?

Thanks! I've been trying to tackle this problem in my head for a while now!

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[Rabolisk]

The direction of the electric force exerted by the electric field isn't perpendicular to the direction of movement of the charged particle. The direction of movement is to top right, since the electron is originally moving to the right, but then is deflected upwards. Draw a diagram and you will see what I mean. It is true that at the second the electron enters the area between the plates, the force is perpendicular to the direction of the motion. However, as soon as the electron changes its direction in response to that force, they are no longer perpendicular.

The difference between this and magnetic field is that the force exerted as a result of a magnetic field is always perpendicular to the direction of motion of a charged particle. Remember F = qV x B. Cross multiplication of two vectors always results in a vector that is orthogonal to both. Imagine an electron moving in a circle as a result of applied magnetic field. As the electron moves, the direction of the force is constantly changing. We say that the direction is always center-seeking, but realize that the direction of the center is changing with respect to the particle's position.

So to find work done by the electric field, the formula to use is W = -qV, and V = Ed. Remember the definition of electric potential, V = U/q. Electrostatic forces being conservative, total mechanical energy is conserved, and work converts potential energy into kinetic energy. Hence W = -deltaU = -delta qV = -delta qEd.

In the case of a magnetic field. realize that while direction of a charged particle changes, its speed does not. That means no potential energy is converted into kinetic energy. Sorry for the length, but I hope this helps!