If a charged particle (charge q) is moving in a circle of radius R at a uniform speed v, then the value of its

Question

If a charged particle (charge q) is moving in a circle of radius R at a uniform speed v, then the value of its associated magnetic moment μ will be:

Accepted Answer

1. **Current Equivalent:** A charged particle $q$ moving in a circle constitutes a current $I$. The current is the rate of flow of charge: $I = q/T$, where $T$ is the time period of revolution .
2. **Time Period:** For a particle moving with speed $v$ in a circle of radius $R$, the time period is $T = \frac{2\pi R}{v}$.
   Substituting this into the current equation: 
   $$I = \frac{q}{2\pi R / v} = \frac{qv}{2\pi R}$$
3. **Magnetic Moment Formula:** The magnetic dipole moment $\mu$ associated with a current loop is given by $\mu = I 	imes A$, where $A$ is the area of the loop .
   $$A = \pi R^2$$
4. **Calculation:** Substituting the expressions for $I$ and $A$:
   $$\mu = \left( \frac{qv}{2\pi R} ight) (\pi R^2)$$
   $$\mu = \frac{qvR}{2}$$

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