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A long wire having a semi-circular loop of radius r carries a current I, as shown in Fig. Find the magnetic field due to entire wire.

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A wire loop formed by joining two semicircular wires of radii R_1 and R_2 carries a current I as shown in figure. Find the magnetic field induction at the centre O.

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Knowledge Check

  • A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is

    A
    `(mu_(0)i)/(4r)`
    B
    `(mu_(0)i)/(2r)`
    C
    `(mu_(0)i)/(2pir) (pi+1)`
    D
    `(mu_(0)i)/(2pir) (pi-1)`

  • The wire loop PQRS formed by joining two semi circular wires of radii R_(1) , and _(2) Ry carries a current I as shown the figure. The inagnitude of magnetic induction at the centre O is

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

  • Two very long, straight wires carrying, currents as shown in Fig. Find all locations where the net magnetic field is zero.

    A
    `y=sqrt2x`
    B
    `y=x`
    C
    `y=-x`
    D
    `y=-(x/2)`

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    A straight wire carrying a current of 12 A is bent into a semi-circular are of radius of 2.0 cm as shown in the adjoining figure (a). Consider the magnetic field B at the centre of the arc. Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way a shown in figure (b)?

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