Respuesta :
Answer:
[tex]\sigma=3.38\times 10^{-6}\ C/m^2[/tex]
Explanation:
Given that,
Mass of the amber bead, m = 12.6 g = 0.0126 kg
Charge on the bead, [tex]q=-0.646\ \mu C=-0.646\times 10^{-6}\ C[/tex]
The electric field due to infinite large plastic sheet is given by :
[tex]E=\dfrac{\sigma}{2\epsilon_o}[/tex]
At equilibrium, q E = m g
[tex]\dfrac{q \sigma}{2\epsilon_o}=mg[/tex]
where
[tex]\sigma[/tex] is the charge per unit area on the glass sheet.
[tex]\sigma=\dfrac{2mg\epsilon_o}{q}[/tex]
[tex]\sigma=\dfrac{2\times 0.0126 \times 9.8\times 8.85\times 10^{-12}}{-0.646\times 10^{-6}}[/tex]
[tex]\sigma=-3.38\times 10^{-6}\ C/m^2[/tex]
So, the charge per unit area on the glass sheet is ([tex]-3.38\times 10^{-6}\ C/m^2[/tex]). Hence, this is the required solution.
Charge per unit area is the electric charge per unit length.
The value if the charge per unit area on the glass sheet is [tex]-3.38\times10^{-6}\rm C/m^2[/tex]
What is charge per unit area?
Charge per unit area is the electric charge per unit length. It can be given as,
[tex]\sigma =\dfrac{2mg\varepsilon_0 }{q}[/tex]
Here [tex]m[/tex] is the mass of the body, [tex]g[/tex] is the gravity, [tex]q[/tex] is the charge and is the [tex]\varepsilon_0[/tex] vacuum permittivity ([tex]8.85\times10^{-12}[/tex]).
Given information-
The mass of the amber bead is 12.6 g or 0.0126 kg.
The charge on the amber bead is -0.646 micro C or [tex]0.646\times10^{-6} C[/tex].
Put the values in the above formula to find the charge per unit area as,
[tex]\sigma =\dfrac{2mg\varepsilon_0 }{q}\\\sigma =\dfrac{2\times0.0126\times9.8\times8.85\times10^{-12}}{-0.646\times10^{-6}}\\\sigma=-3.38\times10^{-6}\rm C/m^2[/tex]
Hence the value if the charge per unit area on the glass sheet is [tex]-3.38\times10^{-6}\rm C/m^2[/tex]
Learn more about the charge per unit area here;
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