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**.

- If the conductors are flowing in the

#### 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