A long wire carrying I=1.3A of constant current oriented East-to-West (and the current is running eastwards) is placed distance d=0.8cm over the top of a compass needle. Assuming the Earth magnetic field to be BEarth= 29μT what is the absolute value of the angular deviation θ of the compass needle from the North-to-South direction?
Question
Answer:
Explanation:
Magnetic field due to a long wire
= 10⁻⁷ x 2i / r where i is current in the wire and r is distance of the point from the wire
In the given case magnetic field
B = 10⁻⁷ x 2i / r
= 10⁻⁷ x 2x 1.3 / .8 x 10⁻²
= 3.25 x 10⁻⁵ T
= 32.5 x 10⁻⁶ T
It will create a deflecting torque on the compass needle
Let after turning by angle θ , equilibrium point is reached
at this point , deflecting torque = restoring torque by earth’s magnetic field
MB cosθ = MHsinθ , M is magnetic moment of magnetic needle , H is horizontal component of earth’s magnetic field.
Tanθ = B / H
= 32.5 / 29
=1.20
θ = 50 degree approx .