Figure shows two long parallel wires separated by a distance of 18 cm. There is current of 8 A in wire 1 and 12 A in wire 2 . At what point on line joining of the wires, the magnetic field is zero?

Question

Figure shows two long parallel wires separated by a distance of 18 cm. There is current of 8 A in wire 1 and 12 A in wire 2 . At what point on line joining of the wires, the magnetic field is zero? (A) 5.2 cm from wire 1 (B) 9.4 cm from wire 2 (C) 7.2 cm from wire 1 (D) 10.3 cm from wire 2

Tardigrade Admin · Accepted Answer

The field is zero between the wires then

\frac{I _{1}}{I _{2}} = \frac{r _{1}}{r _{2}}

\frac{I _{2}}{I _{1}} = \frac{r _{2}}{r _{1}}

= \frac{12}{8} = 1.5

r_{2} = \frac{3}{2} r_{1}

r_{1} + r_{2} = 18

r_{1} + 1.5 r_{1} = 18

∴ r_{1} = \frac{18}{2.5} = 7.2 c m

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Q. Figure shows two long parallel wires separated by a distance of 18cm. There is current of 8A in wire 1 and 12A in wire 2. At what point on line joining of the wires, the magnetic field is zero?

5.2 cm from wire 1

9.4 cm from wire 2

7.2 cm from wire 1

10.3 cm from wire 2

The field is zero between the wires then I2​I1​​=r2​r1​​ I1​I2​​=r1​r2​​ =812​=1.5 r2​=23​r1​ r1​+r2​=18 r1​+1.5r1​=18 ∴r1​=2.518​=7.2cm from 1

Q. Figure shows two long parallel wires separated by a distance of $18 c m$ . There is current of $8 A$ in wire $1$ and $12 A$ in wire $2.$ At what point on line joining of the wires, the magnetic field is zero?

The field is zero between the wires then

$\frac{I _{1}}{I _{2}} = \frac{r _{1}}{r _{2}}$
$\frac{I _{2}}{I _{1}} = \frac{r _{2}}{r _{1}}$
$= \frac{12}{8} = 1.5$
$r_{2} = \frac{3}{2} r_{1}$
$r_{1} + r_{2} = 18$
$r_{1} + 1.5 r_{1} = 18$
$∴ r_{1} = \frac{18}{2.5} = 7.2 c m$ from $1$