Magnetic field at the centre of a circualr loop of area A carrying current I is B. What is the magnetic moment of this loop?

Question

Magnetic field at the centre of a circualr loop of area A carrying current I is B. What is the magnetic moment of this loop?

Magnetic field at the centre of a circualr loop of area A carrying current I is B. What is the magnetic moment of this loop?
A. `((BA)^(2))/(mu_(0)pi)`
B. `(BAsqrtA)/(mu_(0))`
C. `(BA sqrtA)/(mu_(0)pi)`
D. `(2BAsqrtA)/(mu_(0)sqrtpi)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
Let r be the radius of the circular loop.
`therefore" "A=pir^(2) or r=sqrt((A)/(pi))`
Magnetic field at the centre of the loop is
`B=(mu_(0)I)/(2r)=(mu_(0)I)/(2sqrt((A)/(pi)))orI=(2B)/(mu_(0))sqrt((A)/(pi))`
The magnetic moment of the loop is
`M=IA=(2B)/(mu_(0))sqrt((A)/(pi))A=(2BAsqrtA)/(mu_(0)sqrtpi)`