Respuesta :
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 .
The absolute value of the angular deviation θ of the compass needle from the North-to-South direction is; θ = 58.39°
We are given;
Current = 1.3 A
Distance; r = 0.8 cm = 0.008 m
Magnetic field = 20μT = 20 × 10⁻⁶ T
Formula for Magnetic field is;
B = μ_o*I/(2πr)
Where;
μ_o = 4π × 10⁻⁷ H/m
Plugging in the relevant values;
B = (4π × 10⁻⁷ × 1.3)/(2π × 0.008)
B = 32.5 μT
Formula for the angular deviation θ is;
θ = tan^(-1) 32.5/20
θ = 58.39°
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