Respuesta :
Answer:
The maximum value of the induced magnetic field is [tex]2.901\times10^{-13}\ T[/tex].
Explanation:
Given that,
Radius of plate = 30 mm
Separation = 5.0 mm
Frequency = 60 Hz
Suppose the maximum potential difference is 100 V and r= 130 mm.
We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega=2\pi f[/tex]
Put the value into the formula
[tex]\omega=2\times\pi\times60[/tex]
[tex]\omega=376.9\ rad/s[/tex]
When r>R, the magnetic field is inversely proportional to the r.
We need to calculate the maximum value of the induced magnetic field that occurs at r = R
Using formula of magnetic filed
[tex]B_{max}=\dfrac{\mu_{0}\epsilon_{0}R^2\timesV_{max}\times\omega}{2rd}[/tex]
Where, R = radius of plate
d = plate separation
V = voltage
Put the value into the formula
[tex]B_{max}=\dfrac{4\pi\times10^{-7}\times8.85\times10^{-12}\times(30\times10^{-3})^2\times100\times376.9}{2\times130\times10^{-3}\times5.0\times10^{-3}}[/tex]
[tex]B_{max}=2.901\times10^{-13}\ T[/tex]
Hence, The maximum value of the induced magnetic field is [tex]2.901\times10^{-13}\ T[/tex].
