The magnetic moments associated with two closely wound circular coils A and B of radius cm and cm respectively are equal if (where and are number of turns and current of A and B respectively). [2023]

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Q.
The magnetic moments associated with two closely wound circular coils A and B of radius $r_{A} = 10$ cm and $r_{B} = 20$ cm respectively are equal if (where $N_{A}, I_{A}$ and $N_{B}, I_{B}$ are number of turns and current of A and B respectively). [2023]

1 $2 N_{A} I_{A} = N_{B} I_{B}$

2 $N_{A} = 2 N_{B}$

3 $N_{A} I_{A} = 4 N_{B} I_{B}$

4 $4 N_{A} I_{A} = N_{B} I_{B}$

Ans.
(3)

$M = N I A$

$M_{A} = M_{B}$

$∴$ $N_{A} I_{A} A_{A} = N_{B} I_{B} A_{B}$

$∴$ $N_{A} I_{A} π {(0.1)}^{2} = N_{B} I_{B} π {(0.2)}^{2}$

$∴$ $N_{A} I_{A} = 4 N_{B} I_{B}$

Solution

Q.
The magnetic moments associated with two closely wound circular coils A and B of radius $r_{A} = 10$ cm and $r_{B} = 20$ cm respectively are equal if (where $N_{A}, I_{A}$ and $N_{B}, I_{B}$ are number of turns and current of A and B respectively). [2023]

1 $2 N_{A} I_{A} = N_{B} I_{B}$

2 $N_{A} = 2 N_{B}$

3 $N_{A} I_{A} = 4 N_{B} I_{B}$

4 $4 N_{A} I_{A} = N_{B} I_{B}$

Ans.
(3)

$M = N I A$

$M_{A} = M_{B}$

$∴$ $N_{A} I_{A} A_{A} = N_{B} I_{B} A_{B}$

$∴$ $N_{A} I_{A} π {(0.1)}^{2} = N_{B} I_{B} π {(0.2)}^{2}$

$∴$ $N_{A} I_{A} = 4 N_{B} I_{B}$

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Solution

Q. The magnetic moments associated with two closely wound circular coils A and B of radius rA=10 cm and rB=20 cm respectively are equal if (where NA,IA and NB,IB are number of turns and current of A and B respectively). [2023]

1 2NAIA=NBIB

2 NA=2NB

3 NAIA=4NBIB

4 4NAIA=NBIB

Ans. (3) M=NIA MA=MB ∴ NAIAAA=NBIBAB ∴ NAIAπ(0.1)2=NBIBπ(0.2)2 ∴ NAIA=4NBIB

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Q.
The magnetic moments associated with two closely wound circular coils A and B of radius $r_{A} = 10$ cm and $r_{B} = 20$ cm respectively are equal if (where $N_{A}, I_{A}$ and $N_{B}, I_{B}$ are number of turns and current of A and B respectively). [2023]

1 $2 N_{A} I_{A} = N_{B} I_{B}$

2 $N_{A} = 2 N_{B}$

3 $N_{A} I_{A} = 4 N_{B} I_{B}$

4 $4 N_{A} I_{A} = N_{B} I_{B}$

Ans.
(3)

$M = N I A$

$M_{A} = M_{B}$

$∴$ $N_{A} I_{A} A_{A} = N_{B} I_{B} A_{B}$

$∴$ $N_{A} I_{A} π {(0.1)}^{2} = N_{B} I_{B} π {(0.2)}^{2}$

$∴$ $N_{A} I_{A} = 4 N_{B} I_{B}$