# as shown in figure, potential difference V exists between two parallel plates (a,b) that have a small hole. Uniform electric field `vecE` and magnetic flux density `vecB` exist in the region...

as shown in figure, potential difference V exists between two parallel plates (a,b) that have a small hole. Uniform electric field `vecE` and magnetic flux density `vecB` exist in the region above the plates, and are perpendicular to each other. The direction of `vecE` is parallel to this page and plate b. The direction of `vecB` is perpendicular to this page, from back to front. A positively charged particle of charge q and mass m, initially at rest in the hole of plate a, is accelerated by potential difference V so that it enter the region above the plate perpendicularly to `vecE` and `vecB` and travels straight through the region``

what is the ratio of the magnitude E of the electric field to the magnitude B of the magnetic flux density E/B?

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### 1 Answer

The particle is accelerated from rest by the potential difference U until it reaches a speed v when it exits the space between plates (a,b).

Kinetic energy when particle leaves the plates = Electric potential energy given between plates

`(m*v^2)/2 =q*U`

`v = sqrt((2*q*U)/m)`

Now, in the region where there exist both fields **E** and **B** the Lorentz force on the charge q is (v is perpendicular to both E and B):

`F = q*(E +vB)`

Condition of non-deflection is

`F =0` or equivalent `E = -vB` which means that in absolute

value the ratio E/B is

`E/B = v = sqrt((2*q*U)/m)`

Observation:

In practice this experiment is used to determine the rapport (q/m) for the electron or any given particle of charge q and mass m, by measuring the fields E and B under zero deflection conditions.

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