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A loop in the shape of an equilateral tr...

A loop in the shape of an equilateral triangle triangle of side a carries a current `I` as shown in the figure.Find out the magnetic field at the centre `C` of the triangle.

Text Solution

Verified by Experts

The correct Answer is:
`(9mu_(0)i)/(2pia)`
`B=B_(1)+B_(2)+B_(3)=3B_(1)`
`=3(mu_(0))/(4pi)xx(i)/((overset(a)(2sqrt3)))xx(sin60^(@)+sin 60^(@))=(9mu_(0)i)/(2pia)`
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Knowledge Check

  • A conducting wire of length L is bent in the form of an equilateral triangle. If current I is made to pass through it, then calculate the magnetic field intensity at the centre of the triangle.

    A
    `( 27 mu_(0)I)/(4 pi L) `
    B
    `(27 mu_(0)I)/(2 pi L)`
    C
    `(27 mu_(0)I)/(5 pi L)`
    D
    `(27 mu_(0) I)/(7 pi L)`

  • The wire loop shown in figure carries a current as shown. The magnetic field at the centre O is ,

    A
    zero
    B
    `(mu_(0) I)/(4) ((1)/(R_(1)) - (1)/(R_(2)))`
    C
    `(mu_(0)I)/(4) ((1)/(R_(2)) + (1)/(R_(1)))`
    D
    `(mu_(0) I)/(2) ((1)/(R_(1)) - (1)/(R_(2)))`

  • An equilateral triangular loop of wire of side / carries a current I. The magnetic field produced at the circumcentre of the loop is

    A
    `(mu_(0))/(4pi) (3sqrt3I)/(I)`
    B
    `(mu_(0))/(4pi) (9I)/(I)`
    C
    `(mu_(0))/(4pi) (18I)/(I)`
    D
    `(mu_(0))/(4pi) (6I)/(I)`

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