What Magnetic Field Direction Will Allow the Electrons to Pass Through Without Being Deflected?

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What Magnetic Field Direction Allows Electrons to Pass Without Being Deflected?

What Magnetic Field Direction Will Allow the Electrons to Pass Through Without Being Deflected?

šŸ§² Magnetic Force on a Charged Particle

The magnetic force acting on a moving charged particle is governed by the equation:

ā†’F = q (ā†’v Ɨ ā†’B)

For electrons, the charge q is negative, that is:

q = āˆ’e

Hence, the magnetic force on an electron becomes:

ā†’F = āˆ’e (ā†’v Ɨ ā†’B)

šŸ“ Condition for No Deflection

The cross product ā†’v Ɨ ā†’B equals zero when the velocity vector ā†’v and magnetic field vector ā†’B are parallel or anti-parallel:

ā†’v āˆ„ ā†’B or ā†’v anti-parallel to ā†’B ā‡’ ā†’v Ɨ ā†’B = ā†’0

Therefore, the magnetic force becomes:

ā†’F = āˆ’e (ā†’0) = ā†’0

āœ… Final Conclusion

Conclusion: When the magnetic field is directed along the direction of electron motion or exactly opposite to it, the cross product is zero. As a result, no magnetic force acts on the electrons, and they pass through the magnetic field without deflection.

This is a critical concept in electromagnetic theory and is often used in designing devices like velocity selectors, cathode ray tubes, and particle accelerators.

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