Question

An infinitely long wire is placed near a square loop as shown in the figure. Choose the correct options.

• A. The mutual inductance between the two is $\frac{{\mu }_{0}a}{2\pi }\ln \left(2\right)$
• B. The mutual inductance between the two is $\frac{{\mu }_0{a}^2}{2\pi }\ln \left(2\right)$
• C. If a constant current is passed in the straight wire in upward direction and loop is brought close to the wire then induced current in the loop is clockwise
• D. In the above condition, induced current in the loop is anticlockwise

Answer 1

Answer: (A), (C)

The correct options are
A The mutual inductance between the two is $\frac{{\mu }_{0}a}{2\pi }\ln \left(2\right)$
C If a constant current is passed in the straight wire in upward direction and loop is brought close to the wire then induced current in the loop is clockwise

(a) $B_x=\frac{{\mu }_0}{2\pi }\frac{i}{x}$

$d\varphi =\left(B_x\right)dS=\left(\frac{{\mu }_0}{2\pi }\frac{i}{x}\right)\left(adx\right)$

$\varphi ={\int }_a^{2a}d\varphi =\frac{{\mu }_{0}ia}{2\pi }\ln 2$

$M=\frac{\varphi }{i}=\frac{{\mu }_{0}a}{2\pi }\ln 2$

(c) Wire produces $⨀$ magnetic field over the loop. if the loop is brought closer to the wire $⨀$ magnetic field passing through the loop increases. Hence induced current produces $⨂$ magnetic field so, induced current is clockwise.