Question
Asked Nov 14, 2019
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What is the line integral of B  between points i and f in the figure? (Figure 1) Assume that I = 1.4 A .
 
Express your answer using two significant figures.
 
1.0 cm
Integration
path
f
i
I
6.0 cm
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1.0 cm Integration path f i I 6.0 cm

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Expert Answer

Step 1

Given:

Current flowing in the wire = 1.4 A

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1.0 cm Integration path f i I 6.0 cm

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Step 2

Calculating the line integral of B for straight wire portions:

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Line inetrgral of magnetic field is defined as B.dL So, Line integral for the straight portions of the wire (i.e iA and Bf) will be zero, because Mafnetic field is perpendicular to the wire, hence B.dL will become zero.

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Step 3

Line integral for the curve portion ...

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See diagram, let's choose a small element of length dL on the curve path T1cm ode A Magnetic field at the position of small element, B 2Tr Line integral of the magnetic field, B.dL dL 2r From the diagram, dL=rde de Hence, line integral becomes, B.dL 2T Applying the limits of the theta, B.dL d 0 I'n 2 B.dL 7-0 2T 2T BdL 2 4,I47x10x1.4, Ts Substituting the values,B.dL 2 B.dL 8.8x10 Tm

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Science

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Magnetic Effects of Current

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