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Q.

Two long parallel wires are separated by a distance of 8 cm carry electric currents of 3A and 5 A. The distance of null point from the conductor carrying larger current when currents are flowing in the same direction is

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a

3 cm

b

5 cm

c

12 cm

d

20 cm

answer is B.

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Detailed Solution

Question Image

$(\begin{matrix} d_{2} = x \\ d_{1} = r - x \end{matrix})$

$B_{1} = \frac{μ_{0}}{2 π} \frac{i_{1}}{d_{1}}$

$B_{2} = \frac{μ_{0}}{2 π} \frac{i_{2}}{d_{2}}$

$\frac{μ_{0} i_{1}}{2 π (r - x)} = \frac{μ_{0} i_{2}}{2 π x}$

$\frac{i_{1}}{r - x} = \frac{i_{2}}{x}$

$\frac{3}{r - x} = \frac{5}{x}$

$5 (r - x) = 3 x$

$5 r - 5 x = 3 x$

$5 r = 8 x$

$5 \times 8 = 8 x$

$x = 5 cm$

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Two long parallel wires are separated by a distance of 8 cm carry electric currents of 3A and 5 A. The distance of null point from the conductor carrying larger current when currents are flowing in the same direction is