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>>Class 12
>>Physics
>>Moving Charges and Magnetism
>>Force Between Two Current Carrying Parallel Wires and Sheets
>> $The magnitude of force per unit length o$

Question

The magnitude of force per unit length on a wire carrying current $I$ at O due to two semi infinite wires as shown in figure, (if the distance between the long parallel segments of the wire being equal to $L$ and current in them is $I$ ) is:

24049

A

$\frac{+ μ _{0} I ^{2}}{π L} \hat{j}$

B

$\frac{- μ _{0} I ^{2}}{L} \hat{j}$

C

$\frac{μ _{0} I ^{2}}{2 L} \hat{j}$

D

$\frac{μ _{0} I ^{2}}{L} \hat{j}$

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Solution

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Correct option is A)

Net Magnetic field at point O due to both the wires shall be
$B = - 2 \int_{9 0^{0}}^{0^{0}} \frac{μ _{0} I}{2 π l} sin θ d θ$ along $- k$

$∴ B = - \frac{μ _{0} I}{π l}$ along $- k$

Now, $F = I (d l \times B)$
Where, $d l$ is along $i$
Therefore, $\frac{F}{d l} = \frac{μ I ^{2}}{π l}$ along $j$

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