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Numerical

Give an account of magnetic Lorentz force.

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#### Solution

**(a)**

**(b)**

Direction of the Lorentz force on

(a) positive charge

(b) negative charge

- An electric charge q is moving with velocity `vec"v"` in the magnetic field `vec"B"`, experience a force called magnetic force `vec"F"_"m"` deduced by Lorentz.

`vec"F"_"m" = "q" (vec"v" xx vec"B")` ....(1)

`vec"F"_"m"` = qvBsin θ ……………(2)Equations (1) & (2) implies

- `vec"F"_"m"` is directly proportional to the magnetic field `vec"B"`.
- `vec"F"_"m"` is directly proportional to the velocity `vec"V"`.
- `vec"F"_"m"` is directly proportional to sine of the angle between the velocity and magnetic field.
- `vec"F"_"m"` is directly proportional to the magnitude of the charge q.
- `vec"F"_"m"` is always perpendicular to `vec"V" and vec"B".`
- The direction `vec"F"_"m"` on negative charge is opposite to the direction of `vec"F"_"m"` on positive charge.
- If velocity `vec"v"` of the charge is along magnetic field, `vec"F"_"m" = 0.`

Concept: Lorentz Force

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