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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism3 Marks
Question
Two long straight parallel conductors carry steady current $I_1$ and $I_2$ separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.
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Answer



As shown in Figure, the direction of force on conductor b is attractive.
Alternate Answer
$\overrightarrow{\text{B}}$at a point on wire 2, is along - $\hat{\text{k}}$
$\therefore\overrightarrow{\text{F}} , $ on wire 2, due to the $\overrightarrow{\text{B}}$ is along - $\hat{\text{i}}$ i.e.towards wire1. Hence the force is attractive.

Magnetic field, due to current in conductor a,
$\text{B}_{1} = \frac{\mu_\circ\text{I}_{1}}{2\pi\text{d}}$
The magnitude of force on a length L of conductor b,
$\text{F}_{2} = \text{I}_{2}\text{LB}_{1}$
$\text{F}_{2} =\frac{\mu_\circ\text{I}_{1}\text{I}_{2}\text{L}}{2\pi\text{d}}$
One ampere is that steady current which, when maintained in each of the two very long, straight, parallel conductors, placed one meter apart in vacuum, would produce on each of these conductors a force equal to $2 \times10^{-7}$ newton per meter of their length.

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