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Asked Oct 28, 2019
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Two very long wires are parallel to each other separated by a distance d.  The same current flows through each wire but in opposite directions.  See the arrows in the diagram.  Let I = 1 Amp and d = 0.1 meter.

a)  What is the direction of the net magnetic field due to the two, long wires in the space between the wires? Explain your answer.

b)  Calculate the magnitude of the net field at point P, which is half-way between the wires.

c)  Calculate the magnitude of the magnetic force per unit length due to wire #1 on #2.

d)  Determine the direction of the force calculated in part (c) and explain your answer.

#2
P
d
#1
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#2 P d #1

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Expert Answer

Step 1

Given:

Current in the wire, I = 1 amp

Length of the wire, d = 0.1 m

Step 2

(a) Calculating the direction of net magnetic field due to both wires in the space between them:

Magnetic field due to an infinite current carrying wire, B
27r
Where 'r' is the distance of point from the wire.
Let's assume there is point P between the wire at a distance 'r' from the wire 1
(out of the paper)
2Tr
Magnetic field at point P due to wire 1, B
д,1
-(out of the paper)
2л (d -r)
Magnetic field at point P due to wire 2, B
Total magnetic field at point P, B
B +B
(out of the paper)
2πτ 2π(d - r)
B=4I
2л
Id
2r(d-r)
1
r (d-r)
Hence, direction of net magnetic field is out of the paper
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Magnetic field due to an infinite current carrying wire, B 27r Where 'r' is the distance of point from the wire. Let's assume there is point P between the wire at a distance 'r' from the wire 1 (out of the paper) 2Tr Magnetic field at point P due to wire 1, B д,1 -(out of the paper) 2л (d -r) Magnetic field at point P due to wire 2, B Total magnetic field at point P, B B +B (out of the paper) 2πτ 2π(d - r) B=4I 2л Id 2r(d-r) 1 r (d-r) Hence, direction of net magnetic field is out of the paper

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Step 3

(b) Calculating the net magnetic field at ...

Net magnetic field at a point P at a distance r from the wire 1 is, B =
2nr(d-r)
Id
d
d
27T
d
If r,then magnetic field is, B =
2
2
В
ла
2x4x3.14x107 x1
Substituting the values, B =
-8uT
3.14x0.1
B 8uT
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Net magnetic field at a point P at a distance r from the wire 1 is, B = 2nr(d-r) Id d d 27T d If r,then magnetic field is, B = 2 2 В ла 2x4x3.14x107 x1 Substituting the values, B = -8uT 3.14x0.1 B 8uT

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