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A square loop of ABCD carrying a current...

A square loop of ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be

A

`(2mu_0 Ii)/(3pi)`

B

`(mu_0 Ii)/(2pi)`

C

`(2mu_0 IiL)/(3pi)`

D

`(mu_0IiL)/(2pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
Force on wire BE will be cancel out by the force on the wire AD.
` F_(AB) = (mu_0 Ii(L) )/(2pi (L//2) ) = (mu_0 Ii)/(pi) ` (attractive)
`F_(CD) = (mu_0 Ii (L) )/(2pi (3L // 2) ) = (mu_o Ii)/(3pi ) ` (repulsive)
` therefore F_("net") = (mu_0 Ii)/(pi) (1 - 1/3) = (2mu_0Ii)/(3pi) `
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Knowledge Check

  • A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be :

    A
    `(2 mu_(0) li)/(3 pi)`
    B
    `(mu_(0)li)/(2 pi)`
    C
    `(2 mu_(0)liL)/(3 pi)`
    D
    `(mu_(0)liL)/(2 pi)`

  • A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be

    A
    `(2m_0liL)/(3 pi)`
    B
    `(mu_0liL)/(2pi)`
    C
    `(2mu_0Ii)/(3pi)`
    D
    `(mu_0Ii)/(2pi)`

  • A square loop ABCD carrying a current i is placed near and coplanar with a long straight conductor XY carrying a current I .

    A
    There is no net force on the loop
    B
    The loop will be attracted by the conductor only if the current in the loop flows clockwise.
    C
    The loop will be attracted by the conductor only if the current in the loop flows anticlockwise.
    D
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