Question

A long wire carrying I=1.1A of constant current oriented North-to-South (and the current is running northwards) is placed horizontally distance d=0.9cm from a compass needle in the same horizontal plane as the compass needle. Assuming the Earth magnetic field to be BEarth= 20μT. What is the absolute value of the angular deviation θ of the compass needle from the North-to-South direction?

Answer 1

The absolute value of the angular deviation is 39.3°.

Step-by-step explanation:

Given that,

Current = 1.1 A

Distance = 0.9 cm

Magnetic field = 20μT

We need to calculate the magnetic field due to wire

Using formula of magnetic field

`B=(\mu_(0)I)/(2\pi d)`

Put the value into the formula

`B=(4\pi*10^(-7)*1.1)/(2\pi*0.9*10^(-2))`

`B=24.4*10^(-6)\ T`

`B=24.4\ \mu T`

We need to calculate the absolute value of the angular deviation

Using formula of direction

`\theta=\tan^(-1)((B_(E))/(B_(w)))`

`\theta=\tan^(-1)((20 \mu)/(24.4 \mu))`

`\theta=39.3^(\circ)`

Hence, The absolute value of the angular deviation is 39.3°.