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प्रश्न
A wire loop of the form shown in the following figure carries a current I. Obtain the magnitude and direction of the magnetic field at P. (Given: `B = (mu_0I)/(4pir) sqrt2` due to
उत्तर
A circular arc AB with a radius R and a straight conductor BCA make up the wire loop. At the centre of the loop P, the arc AB subtends an angle of Φ = 270° = `(3pi)/2` rad. Since PA = PB = R and C is the midpoint of AB, AB = `sqrt2"R"` and AC = CB = `(sqrt2"R")/2 = "R"/sqrt2`.
Therefore, a = PC = `"R"/sqrt2`.
The magnetic inductions at P due to the arc AB and the straight conductor BCA are respectively,
`"B"_1 = mu_0/(4pi) ("I"phi)/"R" and "B"_2 (mu_0)/(4pi) (2"I")/"a"`
Therefore, the net magnetic induction at P is
`"B"_"net" = "B"_1 + "B"_2 = mu_0/(4pi) I [phi/"R" + 2/("R"//sqrt2)]`
`= mu_0/(4pi) "I"/"R" [phi + 2sqrt2]`
= `mu_0/(4pi) "I"/"R" [(3pi)/2 + 2sqrt2]`
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