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

Options

A. the mutul inductance betweenthe two is `(mu_0a)/(2pi) ln (2)`
B. the mutual inductance between the two is `(mu_0)/(2pi) ln (2)`
C. if a constasnt 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 conditions, induced current in the loop is anti clockwise

Answer

A, C

Explanation

a.
`B_x=mu_0/(2pi) i/x`
`dphi=(B_x)dS=(mu_0/(2pi)i/x) (adx)`
`phi=int_a^(2a)dphi=(mu_0ia)/(2pi) ln 2`
`M=phi/i=(mu_0a)/(2pi) ln 2`
c.
Wire produces `o.` magnetic field over the loop. If the loop is brought closer to the wire, `o.` magnetic field passing through the loop increses. Hence, induced current produces `ox` magnetic field so, induced current is clockwise.