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Question

A beam of electrons projected along the +x axis experiences a force due to a magnetic field along the +y-axis. What is the direction of the magnetic field?


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Solution

Step 1: Given Data

The velocity of the electrons =vi^

Force due to the external magnetic field =Fj^

The charge of an electron =-e

Step 2: Formula Used

We know that the force experienced due to a magnetic field is given as

F=qv×B

where q is the charge of the electrons, v is the velocity of the electrons and B is the external magnetic field.

Step 3: Estimate the Magnetic Field

Upon substituting the values we get,

Fj^=-evi^×B

We know that according to the cycle of unit vectors for the cross product we get,

-i^×k^=j^

Therefore, the magnetic field is in the direction of the unit vector k^.

Hence, the direction of the magnetic field is +z axis.


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