Question

A horizontal power line carries a current of 7250 A from south to north. Earth's magnetic field (65.7 µT) is directed toward the north and is inclined downward at 70.0° to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on 140 m of the line due to Earth's field.

Answer 1

Answer:

a) $||\vec F_{B}||=62.664\,N$, b) From east to west.

Explanation:

Vectorially, the magnetic force can be calculed by the following formula:

$\vec F_{B} = i\cdot \vec l\, \times \, \vec B$

The cross product is:

$\vec F_{B} = \left|\begin{array}{ccc}i&j&k\\1015000\,A\cdot m&0\,A\cdot m&0\,A\cdot m\\22.471\times 10^{-6}\,T&-61.738\times 10^{-6}\,T&0\,T\end{array}\right|$

$\vec F_{B} = - 62.664\,N\cdot k$

a) The magnitude of the magnetic force is:

$||\vec F_{B}||=62.664\,N$

b) The direction of the magnetic force is:

From east to west.