Question on: JAMB Physics - 2024
If a charged ion goes through a combined electric field E and magnetic field B, the resultant emergent velocity of the ion is
A
\(\frac{E}{B}\)
B
EB
C
\(\frac{B}{E}\)
D
E-B
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Correct Option: A
The emergent velocity of an ion moving through combined electric and magnetic fields can be understood by considering the forces acting on the ion:
- Electric Force: The electric force on a charge q in an electric field E is given by FE = qE. This force causes the ion to accelerate in the direction of the electric field (for a positive charge) or opposite to the electric field (for a negative charge).
- Magnetic Force: The magnetic force on a charge q moving with velocity v in a magnetic field B is given by FB = qvB sinθ, where θ is the angle between the velocity and the magnetic field. If the electric and magnetic forces are balanced, the ion will move with a constant velocity.
For the ion to pass through the fields undeflected, the electric force and magnetic force must balance each other. Assuming the electric and magnetic fields are perpendicular to each other and to the velocity of the ion, we have:
\[qE = qvB\]
Dividing both sides by qB:
\[v = \frac{E}{B}\]
Therefore, the emergent velocity of the ion is E/B.
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