Two concentric circular coils, one of small radius r. and the other of large radius r2, such that r1

Question

Two concentric circular coils, one of small radius r. and the other of large radius r2, such that r1<< r2, are placed coaxially with centres coinciding. The mutual inductance of the arrangement is (A) (μ0 π r12/r2) (B) (μ0 π r12/2 r2) (C) (μ0 π r22/r1) (D) (μ0 π r22/2 r1)

Tardigrade Admin · Accepted Answer

Let a current I2 flow through the outer circular coil. The field at the center of the coil is B2=(μ0 I2/2 r2) . Since the other co-axially placed coil has a very small radius, B2 may be considered constant over its cross-sectional area. Hence, φ=π r12 B2 φ=(μ0 π r12 I2/2 r2)=M12 ⋅ I2 ⇒ M12=(μ0 π r12/2 r2)

Q. Two concentric circular coils, one of small radius $r$ . and the other of large radius $r_{2}$ , such that $r_{1} << r_{2}$ , are placed coaxially with centres coinciding. The mutual inductance of the arrangement is

$\frac{μ _{0} π r _{1}^{2}}{r _{2}}$

$\frac{μ _{0} π r _{1}^{2}}{2 r _{2}}$

$\frac{μ _{0} π r _{2}^{2}}{r _{1}}$

$\frac{μ _{0} π r _{2}^{2}}{2 r _{1}}$

Q. Two concentric circular coils, one of small radius r. and the other of large radius r2​, such that r1​<<r2​, are placed coaxially with centres coinciding. The mutual inductance of the arrangement is

r2​μ0​πr12​​

2r2​μ0​πr12​​

r1​μ0​πr22​​

2r1​μ0​πr22​​

Q. Two concentric circular coils, one of small radius $r$ . and the other of large radius $r_{2}$ , such that $r_{1} << r_{2}$ , are placed coaxially with centres coinciding. The mutual inductance of the arrangement is

$\frac{μ _{0} π r _{1}^{2}}{r _{2}}$

$\frac{μ _{0} π r _{1}^{2}}{2 r _{2}}$

$\frac{μ _{0} π r _{2}^{2}}{r _{1}}$

$\frac{μ _{0} π r _{2}^{2}}{2 r _{1}}$