Please show all work Physies 151 Magnetic Field Seore: 15 2 R The diagram shows

Question

Please show all work Physies 151 Magnetic Field Seore: 15 2 R The diagram shows a simple single loop circuit consisting of a wire connected to a wire is of uniform cross section. The battery is ideal. There is a steady current of 3.50 A in the wire. battery. The .P Six (A-F) distinct sections of the circuit have been labeled. The length of the long straight section A is 0.800 m. The two short sections B and F each have a length of 0.015 m. The straight segments C and E each have a length of 0.330 m. Section D forms a semicircle with a center of curvature, marked by point P, that lies on the same line as segments C and E. Estimate the magnitude, and state the direction, of the magnetic field at point P due to each of the six marked segments. (Do not answer zero unless the contribution is exactly zero.) A. B. Estimate the magnitude of the net magnetic field at point P and state its direction.

Explanation / Answer

Segment A:

For a long wire of finite length

Magnetic field B = ?oI/4*pi * (sin?1 + sin?2)

here sin?1 = sin?2 = horizontal length/diagonal

horizontal length = length of segment A / 2 = 0.8/2 = 0.4m

diagonal = sqrt(0.4^2 + 0.015^2) = 0.4003 ~ 0.4 m

sin?1 = sin?2 ~ 1

Ba = 10^-7 * 3.5 * (1+1) = 7e-7 T (Direction is perpendicularly inwards the sheet )

Segment B and F:

Now Bb = Bf =  ?oI/4*pi * (sin?1 + sin?2) here sin?1 = 0

sin?2 = length/diagonal length

length = 0.015

diagonal length is calculated above = 0.4m

sin?2 = 0.015/0.4 = 0.0375 ~ 0.04 m

Bb = Bf = 10^-7*3.5*(0 + 0.04) = 1.4e-8 T (Direction perpendicularly inwards sheet of paper)

Segment C and E

B = 0 since Magnetic field at axis of long wire is always 0

Segment D:

Magnetic field due to semi circular ring at centre = ?oI/4*R = 4*pi*10^-7 * 3.5 / (4*R)

R = (length of A - Length of C )/2= 0.8 - 0.33 ~ 0.24 m

Bd = 4*pi*10^-7 * 3.5 / (4*0.24) = 4.58e-6 T (Direction perpendicularly inwards sheet of paper)

part b)

Net B = Ba + Bb + Bc + Bd + Be + Bf = 7e-7 +  1.4e-8 T +0+ 4.58e-6 + 0 + 1.4e-8 T = 5.3 e-6 T

(Direction perpendicularly inwards sheet of paper)

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