Question

A horizontal power line carries a current of 4950 A from south to north. Earth's magnetic field (80.1 µT) is directed toward the north and is inclined downward at 56.0° to the horizontal. Find the (a) magnitude and (b) direction of the magnetic force on 100 m of the line due to Earth's field.

Answer 1

The magnitude of magnetic force is 32.87 N and the direction of force in west.

Step-by-step explanation:

Given that,

Current = 4950 A

Length = 100 m

Magnetic field
`B= 80.1\ mu T`

Inclined angle = 56.0°

(a). We need to calculate the magnitude of magnetic force

Using formula of magnetic

`F=iBl\sin\theta`

Where, B = magnetic field

i = current

l =length

Put the value into the formula

`F=4950*100*80.1*10^(-6)*\sin56^(\circ)`

`F=32.87\ N`

(b). We need to calculate the direction of magnetic field

According to the right hand rule, the direction of the magnetic force is perpendicular to the plane and the magnetic field.

So, The direction of magnetic force is due to west.

Hence, The magnitude of magnetic force is 32.87 N and the direction of force in west.