Explanation:
Given that,
Radius R= 35 mm
Current = 3.5 A
The magnetic field B is proportional to the r.
Magnetic field is maximum ,when r = R
(a). We need to calculate the radius inside the capacitor
[tex]\dfrac{0.80B_{max}}{B_{max}}=\dfrac{r_{1}}{R}[/tex]
[tex]r_{1}=0.80 R[/tex]
[tex]r_{1}=0.80\times35\times10^{-3}[/tex]
[tex]r_{1}=0.028\ m[/tex]
[tex]r_{1}=28\ mm[/tex]
The radius inside the capacitor is 28 mm.
(b). We need to calculate the radius outside the capacitor
[tex]\dfrac{0.80B_{max}}{B_{max}}=(\dfrac{r_2}{R})^{-1}[/tex]
[tex]r_{2}=\dfrac{35}{0.80}[/tex]
[tex]r_{2}=43.75\ mm[/tex]
The radius outside the capacitor is 43.75 mm.
(c). We need to calculate the maximum value
Using formula of magnetic field
[tex]B=\dfrac{\mu_{0}I}{2\pi R}[/tex]
Put the value into the formula
[tex]B=\dfrac{4\pi\times10^{-7}\times3.5}{2\times3.14\times35\times10^{-3}}[/tex]
[tex]B=2.00\times10^{-5}\ T[/tex]
The maximum value of magnetic field is [tex]2.00\times10^{-5}\ T[/tex].
Hence, This is the required solution.
