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A rectangular loop of length 'l' and bre...

A rectangular loop of length `'l'` and breadth `'b'` is placed at a distance of `x` from an infinitely long wire carrying current `'i'` such that the direction of current is parallel to breadth. If the loop moves away from the current wire in a direction perpendicular to it with a velocity `'v'`, the magnitude of the e.m.f. in the loop is: (`mu_(0)=` permeability of free space)

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To solve the problem, we need to find the induced electromotive force (e.m.f.) in a rectangular loop that is moving away from an infinitely long wire carrying current. The steps to derive the expression for the induced e.m.f. are as follows: ### Step-by-Step Solution: 1. **Understand the Setup**: - We have a rectangular loop with length \( l \) and breadth \( b \). - The loop is placed at a distance \( x \) from an infinitely long wire carrying current \( i \). - The loop moves away from the wire with a velocity \( v \) in a direction perpendicular to the wire. ...
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Knowledge Check

  • A square loop of side a is placed at a distance a away from a long wire carrying a current I_(1) . If the loopcarries a current I_(2) as shown in Fig. then the nature of the force and its amount is -

    A
    `(mu_(0)I_(1)I_(2))/(2pia)`, attractive
    B
    `(mu_(0)I_(1)I_(2))/(4pi)`, attractive
    C
    `(mu_(0)I_(1)I_(2))/(4pi)`, repulsive
    D
    `(mu_(0)I_(1)I_(2))/(4pia)`, repulsive
  • A rectangular loop of metallic wire is of length a and breadth b and carries a current i. The magnetic field at the centre of the loop is

    A
    `( mu_(0) i )/( 4pi ) ( 8 sqrt( a^(2) + b^(2)))/( ab ) `
    B
    `( mu_(0) i )/( 4pi ) ( 4 sqrt( a^(2) + b^(2)))/( ab ) `
    C
    `( mu_(0) i )/( 4pi ) ( 2 sqrt( a^(2) + b^(2)))/( ab ) `
    D
    `( mu_(0) i )/( 4pi ) ( sqrt( a^(2) + b^(2)))/( ab ) `
  • A current - carrying square loop is placed near an infinitely long current-carrying wire as shown in the figure. The torque acting on the loop is

    A
    `(mu_0)/(2pi) i_1 i_2 r`
    B
    `(mu_0)/(2pi) i_1 i_2 log_e2`
    C
    `(mu_0)/(2pi) (i_1 i_2 r)/2`
    D
    Zero
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