Answer :
To solve this problem it is necessary to apply the concepts related to Gauss's Law.
Gauss's law establishes that the flow of certain fields through a closed surface is proportional to the magnitude of the sources of that field inside the same surface.
Mathematically it can be expressed as,
[tex]EA = \frac{Q}{\epsilon_0}[/tex]
Where
A = Surface area of Gaussian surface
Q = Charge enclosed by Gaussian surface
[tex]\epsilon_0[/tex]= Permittivity of free space
E = Electric Field
Our values are given as
[tex]E = 100-500 = -400N/C[/tex]
[tex]A = 4\pi r^2 \rightarrw = 4\pi (0.2)^2 = 0.50m^2[/tex]
[tex]\epsilon_0 = 8.854*10^{-12}C/Nm^2[/tex]
Therefore replacing at our equation we can find Q,
[tex]EA = \frac{Q}{\epsilon_0}[/tex]
[tex](-400)(0.50) = \frac{Q}{8.854*10^{-12}}[/tex]
[tex]Q = -1.7708*10^{-9}C[/tex]
Therefore the magnitude of the charge is [tex]-1.7708*10^{-9}C[/tex]
The magnitude of the charge will be [tex]Q=-1.7708\times 10^{-9} C[/tex]
What will be the charge on the surface of the hollow conducting sphere?
To solve this problem it is necessary to apply the concepts related to Gauss's Law.
According to the Gusse law, the flow of certain fields through a closed surface is proportional to the magnitude of the sources of that field inside the same surface.
Mathematically it can be expressed as,
[tex]EA=\dfrac{Q}{\varepsilon }[/tex]
Where
A = Surface area of Gaussian surface
Q = Charge enclosed by Gaussian surface
[tex]\varepsilon[/tex]= Permittivity of free space
E = Electric Field
Our values are given as
[tex]E=100-500=-400\ \dfrac{N}{C}[/tex]
[tex]A=4\pi r^{2} =4\pi (0.2^{2} )= 0.50 \ m^{2}[/tex]
[tex]\varepsilon =8.854\times 10^{-12} \frac{c}{nm^{2} }[/tex]
putting values we get
[tex]EA=\dfrac{Q}{\varepsilon }[/tex]
[tex]Q= \varepsilon EA[/tex]
[tex]Q=(-400)(0.50)(8.854\times10^{12} )[/tex]
[tex]Q=-1.7708\times 10^{-9} C[/tex]
Thus the magnitude of the charge will be [tex]Q=-1.7708\times 10^{-9} C[/tex]
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