20.a circular segment of radius 10 cm,subtends an angle of 60 degree at it's centre.a current of 9 amperes is flowing the=rough it.find the magnitude and direction of magnetic field produced at the centre?
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Apply Biot Savart's law.
Let K1 = (μ i / 4π) = 9 * 10⁻⁷ units
dB = (μ i/4π) dl X r / (r^3) - using vector notation.
here dl and r are perpendicular always. The magnetic flux density (field) at the center is always perpendicular to the wire and radii. So it is perpendicular to the plane of the wire. r = 0.1 m.
dB = K1 dl / r^2
Integrating B = K1 * (pi r / 3) /r^2 = K1 pi /(3 r^2)
B = 9 * 10⁻⁷ * pi / 0.03 = 9.42 * 10⁻⁵ Tesla
Let K1 = (μ i / 4π) = 9 * 10⁻⁷ units
dB = (μ i/4π) dl X r / (r^3) - using vector notation.
here dl and r are perpendicular always. The magnetic flux density (field) at the center is always perpendicular to the wire and radii. So it is perpendicular to the plane of the wire. r = 0.1 m.
dB = K1 dl / r^2
Integrating B = K1 * (pi r / 3) /r^2 = K1 pi /(3 r^2)
B = 9 * 10⁻⁷ * pi / 0.03 = 9.42 * 10⁻⁵ Tesla
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