A wire AB carries a steady current of $6\,\text{A}$ and is lying on a table. Another wire CD carrying $4\,\text{A}$ is held directly above AB at a height of $1\,\text{mm}$. Find the mass per unit length of wire CD so that it remains suspended at its position when left free. Give the direction of the current in CD with respect to that in AB. (Take $g=10\,\text{m s}^{-2}$.)

$\dfrac{m}{\ell}=4.8\times10^{-4}\,\text{kg/m}$; the current in CD must be in the same direction as in AB.

CBSE Class 12 · 2011 · Magnetic Effects of CurrentShort Answer

A wire AB carries a steady current of

6 A

and is lying on a table. Another wire CD carrying

4 A

is held directly above AB at a height of

1 mm

. Find the mass per unit length of wire CD so that it remains suspended at its position when left free. Give the direction of the current in CD with respect to that in AB. (Take

g = 10 m s^{- 2}

Answer: $\frac{m}{ℓ} = 4.8 \times 1 0^{- 4} kg/m$ ; the current in CD must be in the same direction as in AB.

Solution

CD stays suspended when the upward magnetic force per unit length balances its weight per unit length:

\frac{μ _{0}}{2 π} \frac{I _{1} I _{2}}{h} = \frac{m}{ℓ} g .

\frac{m}{ℓ} = \frac{μ _{0} I _{1} I _{2}}{2 π h g} = \frac{2 \times 1 0 ^{- 7} \times 6 \times 4}{1 0 ^{- 3} \times 10} = 4.8 \times 1 0^{- 4} kg/m .

For the force to be attractive (upward on CD, which is above AB), the current in CD must flow in the same direction as in AB.

CBSE Class 12 Board · 2011 · Subjective

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CBSE Class 12 · 2011 · Magnetic Effects of CurrentShort Answer

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