First slide

Force on a charged particle moving in a magnetic field

Question

Two electrons move parallel to each other with equal speed v. The ratio of magnetic and electrical forces between them is

Easy

A

V/ C
B

C /V
C

V²/C²
D

C²/V²

Solution

Electrostatic force $F_{e} = \frac{1}{4 {πε}_{0}} \times \frac{e^{2}}{r^{2}}$
Magnetic force $F_{m} = \frac{μ_{0}}{4 π} (\frac{e^{2} v^{2}}{r^{2}})$
$∴ \frac{F_{m}}{F_{e}} = μ_{0} ε_{0} v^{2} = \frac{v^{2}}{c^{2}} (∵ μ_{0} ε_{0} = 1 / c^{2})$

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