# How would you determine the magnitude of the magnetic force on a 120 m length of line?

## An electric power line carries a current of $1100 A$ in a location where the earth's magnetic field is 6.0 ✕ 10^-5 T. The line makes an angle of 75° with respect to the field.

Nov 23, 2017

$\vec{F} \approx 7.65 N$

#### Explanation:

The magnitude of the magnetic force is given by $\vec{F} = \vec{B} \vec{I} l \sin \theta$, where:

• $\vec{F}$ is the vector value for the magnetic force ($N$)
• $\vec{B}$ is the vector value for the magnetic field strength ($T$)
• $\vec{I}$ is the vector value for the current ($A$)
• $l$ is the length of material being acted upon by the magnetic field ($m$)
• $\theta$ is the angle between the current and magnetic field (hence why the vector arrows are needed)

The arrows are there for the vector values, as $F$, $B$, and $I$ are part of a vector diagram:

Using the equation, we get:
$\vec{F} = \left(6 \cdot {10}^{- 5}\right) \left(1100\right) \left(120\right) \sin 75 \approx 7.65 N$