Question
Asked Oct 27, 2019

An “infinitely” long wire is bent into the shape seen below.  It carries a current of 14 Amps in the direction given by the arrow heads.  The curved part of the wire is a quarter-circle of radius a = 3.0 cm.

a)  Determine the direction of the total magnetic field produced by the wire at the origin. Explain your answer in words.

b)  Calculate the magnitude of the total magnetic field produced by the wire at the origin.

a
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a

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Expert Answer

Step 1

Given values:

Current in the wire, I = 14 A

Radius of the curved part of the wire, a = 3.0 cm = 0.03 m

The magnetic field due to straight wire can be given by the formula:

(sin e -sin )
B =
4πα
Where
a Perpendicular distance from the wire.
Permity of the free space.
Current in the wire.
1
e,0,-Angle made by the ends of the wire
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(sin e -sin ) B = 4πα Where a Perpendicular distance from the wire. Permity of the free space. Current in the wire. 1 e,0,-Angle made by the ends of the wire

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Step 2

The magnetic field at the centre of current carrying loop:

Д.1
В
2a
Where
Radius of the circular loop
a
Magnetic field at the centre of the quarter of the circular loop:
1, Д.1
Д,1
=-
2a
4
8a
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Д.1 В 2a Where Radius of the circular loop a Magnetic field at the centre of the quarter of the circular loop: 1, Д.1 Д,1 =- 2a 4 8a

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Step 3

(a)

From the right-hand thumb rule, the direction of the total magnetic field at the origin would be point into the page.

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