Respuesta :
Answer:
The magnitude of the magnetic field is [tex]8.9\times10^{-19}\ T[/tex]
Explanation:
Given that,
Electric field = 100 V/m
Radius = 4.0 cm
Electric field increase at a rate = 10 V/ms
Radial distance = 10.0 cm
We need to calculate the magnetic field
Using Gauss's law
[tex]\oint{\vec{E}\cdot\vec{dA}}=\phi_{E}[/tex]
[tex]\dfrac{dE}{dt}A=\dfrac{d\phi_{E}}{dt}[/tex]
[tex]\dfrac{dE}{dt}(\pi r^2)=\dfrac{d\phi_{E}}{dt}[/tex]
We need to calculate the [tex]\dfrac{d\phi}{dt}[/tex]
[tex]\dfrac{d\phi}{dt}=10\times\pi\times(4.0\times10^{-2})^2[/tex]
[tex]\dfrac{d\phi}{dt}=0.0503\ Nm^2/C.s[/tex]
According to Ampere Maxwell law
[tex]\oint{\vec{B}\cdot \vec{ds}}=\mu_{0}(I+\epsilon_{0}\dfrac{d\phi_{E}}{dt})[/tex]
[tex]\oint{\vec{B}\cdot\vec{ds}}=\mu_{0}I+\mu_{0}\epsilon_{0}\dfrac{d\phi_{E}}{dt})[/tex]
Electric field is zero inside the circle.
[tex]\oint{\vec{B}\cdot \vec{ds}}=\mu_{0}\epsilon_{0}\dfrac{d\phi_{E}}{dt})[/tex]
[tex]B(2\pi\times10.0\times10^{-2})=4\pi\times10^{-7}\times8.85\times10^{-12}\times0.0503[/tex]
[tex]B=\dfrac{4\pi\times10^{-7}\times8.85\times10^{-12}\times0.0503}{2\pi\times10.0\times10^{-2}}[/tex]
[tex]B=8.9\times10^{-19}\ T[/tex]
Hence, The magnitude of the magnetic field is [tex]8.9\times10^{-19}\ T[/tex]
