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A current /is flowing through the loop. ...

A current /is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is `(mu_(0)I)/("R") times (MA=R,MB=2R, angleDMA=90^(@)`

A

`(5)/(16)` ,but of the plane of the paper.

B

`(5)/(16)`, but into the plane of the paper.

C

`(7)/(16)`,but out of the plane of the paper.

D

`(7)/(16)`,but into the plane of the paper.

Text Solution

Verified by Experts

The correct Answer is:
D
Magnetic field at the centre M due to current through the curved portion DA is

`B=(mu_(0)I)/(4piR)xx((3pi)/(2))` into the plane of the paper
Since point M lies on the axis of the straight portion AB `:.` Magnetic field at the centre M due to current through the curved portion AB is `B_(2)=0`
Magnetic field at the centre M due to current through the curved portion BC is
`B_(3)=(mu_(0)I)/(4pi2R)xx(pi)/(2)`
into the plane of the paper
`=(mu_(0)I)/(4pi2R)` into the plane of the paper
Since point M lies on the axis of the straight portion CD. `:.` Magnetic field at the centre M due to current through the straight portion CD is `B_(4)=0`
`B=B_(1)+B_(2)+B_(3)+B_(4)`
`=(mu_(0)I)/(R)+0+(mu_(0)I)/(16R)+0=(3mu_(0)I)/(8R)+(mu_(0)I)/(16R)=(7mu_(0)I)/(16R)`
`B=(7mu_(0)I)/(16R)` into the plane of the paper
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Knowledge Check

  • A current I is flowing thorugh the loop. The direction of the current and the shape of the loop are as the shown in the figure. The magnetic fild at the centre of the loop is (mu_(0) I)/(R) times (MA = R, MB = 2R, /_DMA = 90^(@))

    A
    `(5)/(16)`, but out of the plane of the paper.
    B
    `(7)/(16)`, but into of the plane of the paper.
    C
    `(5)/(16)`, but into of the plane of the paper.
    D
    `(7)/(16)`, but out of the plane of the paper.

  • A current l flows through a closed loop as shown in figure .The magnetic field at the centre O is

    A
    `(mu_(0)I)/(2piR)(pi-theta+tantheta)`
    B
    `(mu_(0)I)/(2piR)(pi-theta+sintheta)`
    C
    `(mu_(0)I)/(2piR)(theta+sintheta)`
    D
    None of these

  • A square loop of side a carris a current I . The magnetic field at the centre of the loop is

    A
    `(2mu_0Isqrt2)/(pia)`
    B
    `(mu_0Isqrt2)/(pia)`
    C
    `(4mu_0Isqrt2)/(pia)`
    D
    `(mu_0I)/(pia)`

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