Two infinitely long straight wires A₁ and A₂ ...

CBSE Class 12 Physics 2019 Delhi Set 3 Paper

Question : 7 of 8

Marks: +1, -0

Two infinitely long straight wires

A_1

and

A_2

carrying currents

I

and

2 I

flowing in the same direction are kept '

d

' distance apart. Where should a third straight wire

A_3

carrying current

1.5 I

be placed between

A_1

and

A_2

so that it experiences no net force due to

A_1

and

A_2

? Does the net force acting on

A_3

depend on the current flowing through it?

Solution:

Finding the position of third wire

Reason

\Rightarrow \;\; F_1\;=\;\frac{\mu_0}{4 \pi} \;\frac{I \times 1.5 I}{x}

F_2\;=\;\frac{\mu_0}{4 \pi} \;\frac{2 I \times 1.5 I}{(d-x)}

For no force on the conductor

A_3

\frac{\mu_0}{4 \pi} \;\frac{I \times 1.5 I}{x}\;=\;\frac{\mu_0}{4 \pi} \;\frac{2 I \times 1.5 I}{(d-x)}

\frac{1}{x}\;=\;\frac{2}{(d-x)}

3 x\;=d

x\;=\;\frac{d}{3}

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