# Question:Parallel capacitors and electric beams

An electron beam is send perpendicular onto an electric field between two capacitor plates. The electrons got their kinetic engergi by being accelerated through a potential difference V. The potential difference between the capacitor plates are also V.
The distance between the plates is d, and the length of the plates is a in the direction the electrons move. The electric field is uniform between the plates and 0 outside the plates.The electrons do not hit the plates.

Calculate the angle that the electron beam is deflected by the passage through the space between the plates. How does the angle depend on the potential difference?

This may sound stupid, but i have spend an hour just searching for a formula i could use to solve this problem. I have no idea how to get the angle into a formula.

First i would try to fin the electric field.

So first (Q/V)=e0(A/d) isolate to find Q

and the use F=q(E+VxB)

But im not really sure if this even makes any sense, can anyone help me get started?

F=q(E+VxB)

## The Attempt at a Solution

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Hootenanny
Staff Emeritus
Gold Member
Welcome to Physics Forums.

HINT: Can you relate the potential different of the plates to the force acting on the electron?

Okay.

F=qE and Q=CV

gives

F=CVE so that would give me the force that affects the electron beam between the plates. But it still does'nt make much sense, there must also be a magnetic field that i have to consider.

Hootenanny
Staff Emeritus
Gold Member
Okay.

F=qE and Q=CV

gives

F=CVE so that would give me the force that affects the electron beam between the plates. But it still does'nt make much sense, there must also be a magnetic field that i have to consider.
You need to be careful here, Q refers to the charge on the capacitor plates whereas q refers to the charge of the electron. They are two 'unrelated' quantities.

As for the magnetic field, there is no need to consider it here. Yes, the electron produces a magnetic field, but this will not affect the trajectory of the electron since the magnetic field will only affect charges moving relative to the electron.