Respuesta :
Explanation:
It is given that,
Diameter of the circular loop, d = 1.5 cm
Radius of the circular loop, r = 0.0075 m
Magnetic field, [tex]B=2.7\ mT=2.7\times 10^{-3}\ T[/tex]
(A) We need to find the current in the loop. The magnetic field in a circular loop is given by :
[tex]B=\dfrac{\mu_o I}{2r}[/tex]
[tex]I=\dfrac{2Br}{\mu_o}[/tex]
[tex]I=\dfrac{2\times 2.7\times 10^{-3}\times 0.0075}{4\pi \times 10^{-7}}[/tex]
I = 32.22 A
(b) The magnetic field on a current carrying 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 32.22}{2\pi \times 2.7\times 10^{-3}}[/tex]
r = 0.00238 m
[tex]r=2.38\times 10^{-3}\ m[/tex]
Hence, this is the required solution.
The value of current in the loop is 32.22 A and the distance of the current carrying wire from the magnetic field is 2.38×10⁻³m.
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.
The magnetic field experienced by a charged particle can be given as,
[tex]B=\dfrac{\mu_oI}{2r}[/tex]
Here, (I) is the magnitude of current, and (r) is the radius
- A. The current in the loop-
As the diameter of the loop is 1.50 cm or 0.0150 m. Thus, the radius of the loop is 0.0075 m. Here, the magnetic field is 2.70 mT. Plug in the values in the above formula as,
[tex]2.70\times10^{-3}=\dfrac{4\pi\rimes10^{-7}I}{2(0.0075)}\\I=32.22\rm A[/tex]
- B. The distance from the wire is the magnetic field 2.70 mT
The formula for the magnetic field for current carrying wire can be given as,
[tex]B=\dfrac{\mu_oI}{2\pi r}[/tex]
As the values of the current in this case is 32.22 A. Thus put the values as,
[tex]2.70\times10^{-3}=\dfrac{4\pi \times10^{-7}(32.22)}{2\pi r}\\r=2.38\times10^{-3}\rm m[/tex]
Hence, the value of current in the loop is 32.22 A and the distance of the current carrying wire from the magnetic field is 2.38×10⁻³m.
Learn more about magnetic field here;
https://brainly.com/question/7802337
