2. A device called a \"Wien velocity selector\" or an \" filter\" (pronounced \"

Question

2. A device called a "Wien velocity selector" or an " filter" (pronounced "E-cross-B") is often used in particle accelerators, ion-therapy installations, plasma power studies, and experiments on atoms and molecules. (If fancy strikes you, you can buy one, for example, at https://www.dreebit-ibt.com/product/wien-filter.html It works as a velocity selector in which particles of a specific velocity pass through undeflected while those with greater or lesser velocities are deflected either upwards or downwards. An electric field is directed perpendicular to a magnetic field, producing an electric force and a magnetic force on the charged particle that can be equal in magnitude and opposite in direction and hence cancel. Use the formulas for electric and magnetic forces to show that the velocity of particles that pass undeflected must be equal to u=EB. Source Slit

Explanation / Answer

The magnetic field is perpendicular to both the velocity and the electric field.

The magnetic force has equal magnitude and opposite in direction to the electric force.

Fm=qvB

Fe=qE

The forces balance when:

qE = qvB

E = vB

v = E/B

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