Respuesta :
Explanation:
It is given that,
Diameter of loop, d = 1.4 cm
Radius of loop, r = 0.7 cm = 0.007 m
Magnetic field, [tex]B=2.5\ mT=2.5\times 10^{-3}\ T[/tex]
(A) Magnetic field of a current loop is given by :
[tex]B=\dfrac{\mu_oI}{2r}[/tex]
I is the current in the loop
[tex]I=\dfrac{2Br}{\mu_o}[/tex]
[tex]I=\dfrac{2\times 2.5\times 10^{-3}\times 0.007}{4\pi \times 10^{-7}}[/tex]
I = 27.85 A
(B) Magnetic field at a distance r from a wire is given by :
[tex]B=\dfrac{\mu_o I}{2\pi r}[/tex]
[tex]r=\dfrac{\mu_o I}{2\pi B}[/tex]
[tex]r=\dfrac{4\pi \times 10^{-7}\times 27.85}{2\pi \times 2.5\times 10^{-3}}[/tex]
r = 0.00222 m
[tex]r=2.2\times 10^{-3}\ m[/tex]
Hence, this is the required solution.
The magnetic field is the field in the space and around the magnet in which the magnetic field can be fill.
- a) The current flowing in the loop is 27.85 ampere.
- b) The distance from the wire is 0.22 cm.
What is magnetic field?
The magnetic field is the field in the space and around the magnet in which the magnetic field can be fill.
It can be given as,
[tex]B=\dfrac{\mu_0I}{ 2r}[/tex]
Here, [tex]I[/tex] is the current and [tex]r[/tex] is the distance.
Given information
The diameter of the loop is 1.40 cm.
The magnetic field at the center of the loop is 2.50 mT.
- A) The current in the loop-
Put the values in the above formula as,
[tex]2.5\times10^{-3}=\dfrac{4\times\pi \times10^{-7}I}{ 2\times0.007} \\I=27.85\rm A[/tex]
Hence the current flowing in the loop is 27.85 ampere.
- B) The distance from the wire-
Now the distance from wire has to be found for the current value of 27.85.
Let the distance from the wire is [tex]r[/tex]. Thus again put the values in the above formula as,
[tex]2.5\times10^{-3}=\dfrac{4\times\pi \times10^{-7}\times27.85}{ 2\timesr} \\r=0.00222\rm m\\r=0.22\rm cm[/tex]
Thus the distance from the wire is 0.22 cm.
- a) The current flowing in the loop is 27.85 ampere.
- b) The distance from the wire is 0.22 cm.
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