When but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height above the loop. In that case [2014]

Question

The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$ . The loop and the wires are carrying the same current $I$ . The current in the loop is in the counterclockwise direction if seen from above.

Q. When $d \approx a$ but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height $h$ above the loop. In that case [2014]

Smart Achievers · Accepted Answer

(3)

$Here B_{1} \sin θ and B_{2} \sin θ cancelled each other.$

For zero magnetic field at $' P'$

Magnetic field due to current carrying circular loop = Magnetic field due to straight wires

$B = B_{1} \cos θ + B_{2} \cos θ = 2 B_{1} \cos θ$

$\frac{μ_{0} I a^{2}}{2 {(a^{2} + h^{2})}^{3 / 2}} = 2 [\frac{μ_{0} I}{2 π \sqrt{a^{2} + h^{2}}}] \times \frac{a}{\sqrt{a^{2} + h^{2}}}$

Solving we get,

$h \approx 1.2 a$

The current is from P to Q and R to S in wire 1 and wire 2 respectively.

Solution

1 current in wire 1 and wire 2 in the direction PQ and RS, respectively and $h \approx a$

2 current in wire 1 and wire 2 in the direction PQ and SR, respectively and $h \approx a$

3 current in wire 1 and wire 2 in the direction PQ and SR, respectively and $h \approx 1.2 a$

4 current in wire 1 and wire 2 in the direction PQ and RS, respectively and $h \approx 1.2 a$

Want Us to Email you About Special Offers & Updates?

Solution

1 current in wire 1 and wire 2 in the direction PQ and RS, respectively and h≈a

2 current in wire 1 and wire 2 in the direction PQ and SR, respectively and h≈a

3 current in wire 1 and wire 2 in the direction PQ and SR, respectively and h≈1.2a

4 current in wire 1 and wire 2 in the direction PQ and RS, respectively and h≈1.2a

Want Us to Email you About Special Offers & Updates?

1 current in wire 1 and wire 2 in the direction PQ and RS, respectively and $h \approx a$

2 current in wire 1 and wire 2 in the direction PQ and SR, respectively and $h \approx a$

3 current in wire 1 and wire 2 in the direction PQ and SR, respectively and $h \approx 1.2 a$

4 current in wire 1 and wire 2 in the direction PQ and RS, respectively and $h \approx 1.2 a$