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

a)
`||\vec F_(B)||=62.664\,N`, b) From east to west.

Step-by-step explanation:

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

`\vec F_(B) = i\cdot \vec l\, * \, \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* 10^(-6)\,T&-61.738* 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.