Magnetic Force On Charge

Question

Magnitude of magnetic force on charge q moving with velocity v perpendicular to uniform B?

RankGuru · Accepted Answer

1. **Lorentz Force Law**: The magnetic force ($F_m$) on a moving charge $q$ is given by the cross product of velocity and magnetic field vectors: $\vec{F}_m = q (\vec{v} 	imes \vec{B})$.
2. **Magnitude Formula**: The magnitude is $F_m = q v B \sin 	heta$, where $	heta$ is the angle between the velocity and the field.
3. **Identify Condition**: The problem states that the motion is **perpendicular** to the field, so $	heta = 90^\circ$.
4. **Calculation**: Since $\sin 90^\circ = 1$, the expression simplifies to $F_m = q v B 	imes 1$.
5. **Final Result**: The magnitude of the force is **$qvB$**.

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Magnetic Force On Charge

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