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As current I flowing through the loop as...

As current I flowing through the loop as shown in figure. The magnetic field at the centre O is

Text Solution

Verified by Experts

The correct Answer is:
D
The angle, subtended by arc DE at O is `(pi)/(2)` and FC at `O= (3pi)/(2)` the effective magnetic field at O is `B= B_(DE) + B_(FC)`

`=(mu_(0)i)/(4pi 3r)xx (pi)/(2) + (mu_(0)i)/(4pi r) xx ((3pi)/(2))`
`=(mu_(0)i)/(8r) [(1)/(3) + 3]`
`=(5mu_(0)i)/(12r)` acting downwards
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Knowledge Check

  • 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 current I flows through a closed loop as shown in figure. The magnetic field induction at the centre 0 is

    A
    `(mu_(0)I)/(4piR)theta`
    B
    `(mu_(0)I)/(4piR)(theta+sintheta)`
    C
    `(mu_(0)I)/(4piR)(pi-theta+sintheta)`
    D
    `(mu_(0)I)/(4piR)(pi-theta+tantheta)`

  • 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.

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