The Question is from neet-physics magnetic-effects-current-and-magnetism , and it was created by the author NAGA SAI

Question

An electron is moving in a circular orbit of radius 'r' with a constant speed 'v'. What is the magnetic moment associated with its motion?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Magnetic moment of a current loop
 **Related Topics**:  Circular motion, current, magnetic field
 **Prerequisites**: Understanding of current, magnetic moment, and the relationship between current and moving charge.
## SOLUTION PATHWAY
**Given Information**:
  Radius of orbit = r
  Speed of electron = v
  Charge of electron = e (negative, but magnitude is used here)
**Method & Steps**:
 1. Calculate the current due to the electron's motion.
  Reasoning: The electron completes one revolution in time $T = \frac{2\pi r}{v}$.  The current is the charge passing a point per unit time. 
  Formula/Rule: $I = \frac{q}{T} = \frac{e}{\frac{2\pi r}{v}} = \frac{ev}{2\pi r}$ 
 2. Calculate the area of the circular orbit.
  Working: $A = \pi r^2$
  Key Point: The area is important because the magnetic moment depends on the current and the area of the loop.
 3. Calculate the magnetic moment.
  Formula/Rule: The magnetic moment ($\mu$) of a current loop is given by $\mu = IA$.
  Working: $\mu = IA = \left(\frac{ev}{2\pi r}ight)(\pi r^2) = \frac{evr}{2}$
  Result: $\mu = \frac{evr}{2}$
  Verification: Units are consistent: $[A][m^2] = [C/s][m^2] = [C m^2/s]$ which are the units of magnetic moment.
 ## OPTION ANALYSIS
A :x: Incorrect. This option misses the factor of 1/2.
B ✓: Correct. This is the correct formula derived above.
C :x: Incorrect. This option has an extra factor of 2.
D :x: Incorrect. This option has an incorrect combination of r and v.
 ## LEARNING AIDS
 **Common Mistakes**:
  1. Forgetting to calculate the time period and using the charge directly in the current calculation:  Always remember that current is charge per unit time. 
  2. Incorrectly using the area of the loop:  The area must be the area enclosed by the electron's orbit.
 **Quick Tips**:
  1. Remember the formula $\mu = IA$ for the magnetic moment of a current loop. 
  2. Visualize the circular motion of the electron as a current loop to better understand the concept.

NAGA SAI · Answer

evr

NAGA SAI · Answer

The correct Option is "(evr)/2"

NAGA SAI · Answer

2evr

NAGA SAI · Answer

ev/2r

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