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The magnetic field at centre O of the ar...

The magnetic field at centre O of the arc in Fig.

A

`(mu_0I)/(4pixxr)[sqrt2+pi]`

B

`(muI)/(2pir)[pi/4+(sqrt2-1)]`

C

`(mu_0)/(4pi)xxI/r[(sqrt2-pi)]`

D

`(muI)/(4pi)xxI/r[sqrt2+pi/4]`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Magnetic field due to straight wires

`B_(circular)=1/4 (mu_0I)/(2r)=(mu_0I)/(8r)`
`B_(straight)=2(mu_0I)/(4pi(rcos45^@))[sin90^@-sin45^@]`
`=(sqrt2mu_0I)/(2pir)[1-1/sqrt2]`
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Knowledge Check

  • The magnetic field at O is

    A
    zero
    B
    `1`
    C
    `2`
    D
    `3`

  • The magnetic field at O is

    A
    `(mu_(0)I)/(2R)sqrt((1/4+1/(pi^(2))))`
    B
    `(mu_(0)I)/(2R)sqrt((1/2+1/(pi^(2))))`
    C
    `(mu_(0)I)/(R)sqrt((1/4+1/(pi^(2))))`
    D
    `(mu_(0)I)/(R)sqrt((1/4+1/(pi)))`

  • The magnetic field at the centre O of the are shown in the figure is

    A
    `2I(sqrt(2)+pi)xx(10^(-7))/(r)`
    B
    `2I(sqrt(2)+(pi)/(4))xx(10^(-7))/(r)`
    C
    `I(sqrt(2)+pi)xx(10^(-7))/(r)`
    D
    `I(sqrt(2)+(pi)/(4))xx(10^(-7))/(r)`

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