Describe qulitatively and quantitatively the force between long parallel current carrying conductors

Forces between two parallel conductors

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  • When two conductors are placed within a distance of each other, they will experience a force as the magnetic fields around each conductor will interact with each other.
  • When the conductors are parallel, the magnetic fields interact with each other in a way depending on the direction of the current in the conductors.
    • If the conductors are flowing in the same direction, their magnetic fields would join and they would attract each other.
    • If the conductors are flowing in opposite directions, their magnetic fields would repel and the conductors would repel each other.
    • Both of these can be confirmed by the use of the right hand push rule.

Finding the magnitude of the force

Based on the above, we can describe the magnetic interaction of $I_1$ on $I_2$ to be

(1)
\begin{align} B = \frac{kI_2}{d} \end{align}

We also know that the force provided by wire one can be found as $F = BI_1l$

Thus:

(2)
\begin{align} B = \frac{F}{I_1l} \end{align}

Hence, the magnitude of the force can be summed up Mathematically as:

(3)
\begin{align} F = k\frac{I_1I_2l}{d} \end{align}

Where:

  • $B$ is the strength of the External Magnetic Field
  • $k$ is Ampere's constant ($2.00 x 10^{-7}$)
  • $I_1$ and $I_2$are the currents in the first conductor and the second conductor respectively($A$)
  • $l$ is the common/shared length of the conductors ($m$)
  • $d$ is the perpendicular distance between the two conductors ($m$)