A- What is the magnitude of the magnetic field at point P (at the center of the

Question

A- What is the magnitude of the magnetic field at point P (at the center of the triangular loop) due to the current in the wire? Answer in units of µT.

B- If this conductor is formed into a single circular turn and carries the same current, what is the magnitude of the magnetic field at the center? Answer in units of µT.

A conductor in the shape of an equilateral triangle, whose sides are of length 0.585 m carries a counter-clockwise 20.7 A current as shown in the figure below. 7 The permeability of free space 4 x 10 T-m/A 20.7 A 0.585 m--

Explanation / Answer

A)

net magnetic field at point P = 3*B

and B is magnetic field due to a wire at point P

B = u0*I/(2*pi*r)

here r = distance between wire and point P = sqrt((0.585)^2 - (0.585/2)^2) * (1/3) = 0.169 m

so net magnetic field at point P = 3*[(4*pi*10^(-7)*20.7)/(2*pi*0.169)] = 73.49*10^(-6) T = 73.49 uT

B)

If this conductor is formed into a single circular turn

Then magnetic field at point P = B = (4*pi*10^(-7)*20.7)/(2*pi*0.169) = 24.4*10^(-6) T = 24.4 uT

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