Respuesta :
Answer:
1.08 × 10⁻⁶ A
Explanation:
Data provided in the question:
Diameter of the sphere, d = 16 cm
Magnetic field, B = 3.0 pT = 3 × 10⁻¹² T
now,
[tex]B=\frac{\mu_o}{2}\frac{Ir^2}{(z^2+r^2)^{\frac{3}{2}}}[/tex]
here,
z is the point of consideration i.e pole of the sphere from the center
= 16 ÷ 2 = 8 cm
permeability constant = μ₀ = 4π × 10⁻⁷ H/m
I is the current
on substituting the respective values, we get
3 × 10⁻¹² T = [tex]\frac{4\pi\times10^{-7}}{2}\times\frac{I\times8^2}{(8^2+8^2)^{\frac{3}{2}}}[/tex]
or
3 × 10⁻¹² T = [tex]6.28\times\pi\times10^{-7}\times\frac{I\times64}{(1448.15}[/tex]
or
I = 1.08 × 10⁻⁶ A
The amount of current needed to produce the required magnetic field is [tex]1.08\times 10^{-6}\;\rm A[/tex].
What is the magnetic field?
A magnetic field is defined as the magnetic influence on moving electric charges, electric currents, and magnetic materials.
Given that the magnetic field B around the sphere is 3.0 pT and the diameter d of the sphere is 16 cm.
The radius r of the sphere is d/2 which is 8 cm. The distance of the pole from the center of the sphere is assumed as half of the diameter i.e. 8 cm.
[tex]B = \dfrac {\mu_0 \times I}{2(r^2+r'^2)}\times \dfrac {r^2}{\sqrt{r^2+r'^2} }[/tex]
Where I is the current in the metal sphere and r is the radius of the sphere. r' is the distance of the pole from the center of the sphere. The permeability constant [tex]\mu_0[/tex] is [tex]4\pi\times 10^{-7} \;\rm H/m[/tex].
[tex]3\times 10^{-12} = \dfrac {4\times 3.14\times 10^{-7}\times I}{2 \times (0.08^2+0.08^2)} \times \dfrac {0.08^2}{\sqrt{(0.08^2+0.08^2)} }[/tex]
[tex]2.388 \times 10^{-6} = \dfrac {I}{2 \times 0.0128} \times \dfrac {6.4\times 10^{-3}}{0.11313}[/tex]
[tex]I = 1.08 \times 10^{-6}\;\rm A[/tex]
Hence we can conclude that the amount of current needed to produce the required magnetic field is [tex]1.08\times 10^{-6}\;\rm A[/tex].
To know more about the magnetic field, follow the link given below.
https://brainly.com/question/19542022.
