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Find the magnetic field at the centre of...

Find the magnetic field at the centre of the circular loop shown in figure.

Text Solution

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Magnetic field at the point O due to infinite wire is `(mu_(0)i)/(2piR)` out of the plane.
Magnetic field at the point O due to circular loop is `(mu_(0)i)/(2piR)` out of the plane.
Magnetic field at the point O due to circular loop is `(mu_(0)i)/(2R)` into the plane.
Thus net field `=(mu_(0)i)/(2R)[1/(pi)hatk-hatk]=(mu_(0)i)/(2R)[1/(pi)-1]hatk=(mu_(0)i)/(2R)((pi-1)/(pi))(-hatk)`
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Find the magnetic field at the centre O of the loop shown in the figure.

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Knowledge Check

  • The magnetic field at the centre of the circular loop as shown in Fig. when a single wire is bent to form a circular loop and also extends to form straight sections is

    A
    `(mu_0I)/(2R)odot`
    B
    `(mu_0I)/(2R) (1+1/(pisqrt2))odot`
    C
    `(mu_0I)/(2R) (1-1/(pisqrt2))ox`
    D
    `(mu_0I)/R (1-1/(pisqrt2))ox`

  • Magnetic field at the centre of a circular loop of area

    A
    `(BA^(2))/(mu_(0)pi)`
    B
    `(BAsqrtA)/(mu_(0)`
    C
    `(BAsqrtA)/(mu_(0)pi`
    D
    `(2BAsqrtA)/(mu_(0)sqrtpi`

  • 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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