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

Answer:

The absolute value of the angular deviation is 39.3°.

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

$B=\dfrac{\mu_{0}I}{2\pi d}$

Put the value into the formula

$B=\dfrac{4\pi\times10^{-7}\times1.1}{2\pi\times0.9\times10^{-2}}$

$B=24.4\times10^{-6}\ T$

$B=24.4\ \mu T$

We need to calculate the absolute value of the angular deviation

Using formula of direction

$\theta=\tan^{-1}(\dfrac{B_{E}}{B_{w}})$

$\theta=\tan^{-1}(\dfrac{20 \mu}{24.4 \mu})$

$\theta=39.3^{\circ}$

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