Two circular coils P and Q are made from similar wire, but radius of Q is twice that of P . What should be the value of potential difference across them so that the magnetic induction at their centre may be same?

Question

Two circular coils P and Q are made from similar wire, but radius of Q is twice that of P . What should be the value of potential difference across them so that the magnetic induction at their centre may be same? (A)  Vq = 2Vp  (B)  Vq = 3 Vp  (C)  Vq = 4Vp  (D)  Vq = (1/4) Vp

Tardigrade Admin · Accepted Answer

B1=(μ0/4 π)[(2 π I1/r1)] and B2=(μ0/4 π)[(2 π I2/r2)] Since, B1=B2 and r2=2 r1, I2=2 I1 ∴ (V2/V1)=(I2 R2/I1 R1)=(2 I1/I1) × (2 R1/R1)=(4/1)

Q. Two circular coils $P$ and $Q$ are made from similar wire, but radius of $Q$ is twice that of $P$ . What should be the value of potential difference across them so that the magnetic induction at their centre may be same?

$V_{q} = 2 V_{p}$

$V_{q} = 3 V_{p}$

$V_{q} = 4 V_{p}$

$V_{q} = \frac{1}{4} V_{p}$

Q. Two circular coils P and Q are made from similar wire, but radius of Q is twice that of P . What should be the value of potential difference across them so that the magnetic induction at their centre may be same?

Vq​=2Vp​

Vq​=3Vp​

Vq​=4Vp​

Vq​=41​Vp​

B1​=4πμ0​​[r1​2πI1​​] and B2​=4πμ0​​[r2​2πI2​​] Since, B1​=B2​ and r2​=2r1​,I2​=2I1​ ∴V1​V2​​=I1​R1​I2​R2​​=I1​2I1​​×R1​2R1​​=14​

Q. Two circular coils $P$ and $Q$ are made from similar wire, but radius of $Q$ is twice that of $P$ . What should be the value of potential difference across them so that the magnetic induction at their centre may be same?

$V_{q} = 2 V_{p}$

$V_{q} = 3 V_{p}$

$V_{q} = 4 V_{p}$

$V_{q} = \frac{1}{4} V_{p}$