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

#### Forces between two parallel conductors

• 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 ($m$)
page revision: 4, last edited: 16 Feb 2011 14:10