Respuesta :
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
[tex]B=\dfrac{\mu_{0}I}{2\pi d}[/tex]
Put the value into the formula
[tex]B=\dfrac{4\pi\times10^{-7}\times1.1}{2\pi\times0.9\times10^{-2}}[/tex]
[tex]B=24.4\times10^{-6}\ T[/tex]
[tex]B=24.4\ \mu T[/tex]
We need to calculate the absolute value of the angular deviation
Using formula of direction
[tex]\theta=\tan^{-1}(\dfrac{B_{E}}{B_{w}})[/tex]
[tex]\theta=\tan^{-1}(\dfrac{20 \mu}{24.4 \mu})[/tex]
[tex]\theta=39.3^{\circ}[/tex]
Hence, The absolute value of the angular deviation is 39.3°.
The absolute value of the angular deviation (θ) of the compass needle from the North-to-South direction is 50.66°.
Given the following data:
Current, I = 1.1 A
Distance, r = 0.9 cm to m = 0.009 m.
Magnetic field of Earth = 20 μT = 20 × 10⁻⁶ T.
Scientific data:
Permittivity of free space = [tex]4\pi \times 10^{-7}\; T.m/A[/tex]
How to calculate the magnetic field.
Mathematically, the magnitude of a magnetic field is given by this formula:
[tex]B=\frac{\mu_o I}{2\pi r}[/tex]
Where:
- B is the magnetic field.
- I is the current.
- r is the distance.
- [tex]\mu_o[/tex] is the permittivity of free space.
Substituting the given parameters into the formula, we have;
[tex]B=\frac{4\pi \times 10^{-7}\times 1.1}{2\times 3.142 \times 0.009}\\\\B=\frac{1.38 \times 10^{-6}}{0.05656} \\\\B=2.44 \times 10^{-5}[/tex]
B = 24.4 μT.
For the angular deviation, we have:
[tex]\theta = tan^{-1}\frac{B}{B'} \\\\\theta = tan^{-1}(\frac{24.4}{20})\\\\\theta = tan^{-1}(1.22)[/tex]
Angular deviation = 50.66°.
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