Respuesta :
Answer:
[tex]-1.7908787542\times 10^{-9}\ C[/tex]
[tex]3.4260289211\times 10^{-9}\ C[/tex]
[tex]1.7908787542\times 10^{-9}\ C[/tex]
[tex]1.6351501669\times 10^{-9}\ C[/tex]
Explanation:
r = Radius
k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]
Electric field is given by
[tex]E=-\dfrac{kq}{r^2}\\\Rightarrow q=-\dfrac{Er^2}{k}\\\Rightarrow q=-\dfrac{1610\times 0.1^2}{8.99\times 10^9}\\\Rightarrow q=-1.7908787542\times 10^{-9}\ C[/tex]
The charge is [tex]-1.7908787542\times 10^{-9}\ C[/tex]
[tex]Q+q=\dfrac{Er^2}{k}\\\Rightarrow Q=\dfrac{Er^2}{k}-q\\\Rightarrow Q=\dfrac{120\times 0.35^2}{8.99\times 10^9}-(-1.7908787542\times 10^{-9})\\\Rightarrow Q=3.4260289211\times 10^{-9}\ C[/tex]
The charge is [tex]3.4260289211\times 10^{-9}\ C[/tex]
The charge inside will have the polarity changed
[tex]q=+1.7908787542\times 10^{-9}\ C[/tex]
Outside the charge will be
[tex]3.4260289211\times 10^{-9}-1.7908787542\times 10^{-9}\\ =1.6351501669\times 10^{-9}\ C[/tex]
The magnitude of the electric field or force between two charged points is directly proportional to the charge and inversely proportion to the square of the distance between the points.
- The charge on the insulating sphere is [tex]-1.791\times 10^{-9}[/tex] C.
- The net charge on the conducting sphere is [tex]3.426\times 10^{-9}[/tex] C.
- Total charge on the inner surface of the hollow conducting sphere is [tex]1.791\times 10^{-9}[/tex] C.
- The total charge on the outer surface of the hollow conducting sphere is [tex]1.635\times 10^{-9}\\[/tex]
Given information-
The radius of the insulating sphere is 6 cm.
The inner radius of the conducting sphere is 18 cm.
The outer radius of the conducting sphere is 26 cm.
The electric field at a point 10 cm from the center.
The electric field measure is 1610 N/C.
What is electric field?
The magnitude of the electric field or force between two charged points is directly proportional to the charge and inversely proportion to the square of the distance between the points.
Let [tex]q[/tex] is the charge on the insulating sphere. Thus by the definition of electric field-
[tex]E=-\dfrac{kq}{r^2}[/tex]
Here, [tex]k[/tex] is coulomb's constant with value equal to the [tex]8.99\times10^9[/tex] N-m squared per coulomb squared.
- A) The charge on the insulating sphere-
[tex]1610=\dfrac{-8.99\times 10^9q}{0.1^2}\\q=-1.791\times 10^{-9}[/tex]
Hence, the charge on the insulating sphere is [tex]-1.791\times 10^{-9}[/tex] C.
- B) The net charge on the conducting sphere-
Net charge is the sum of the charge on both sphere. Thus,
[tex]Q=\dfrac{E_1r_1^2}{k}+\dfrac{Er^2}{k}\\Q=\dfrac{120\tiems0.35^2}{8.99\times10^9} +(-1.791\times 10^{-9})[/tex]
[tex]Q=3.426\times 10^{-9}[/tex]
Hence, the net charge on the conducting sphere is [tex]3.426\times 10^{-9}[/tex] C.
- C) Total charge on the inner surface of the hollow conducting sphere-
The charge inner surface of the hollow conducting sphere is equal and opposite the charge on the insulating sphere.
Therefore, total charge on the inner surface of the hollow conducting sphere is [tex]1.791\times 10^{-9}[/tex] C.
- D) The total charge on the outer surface of the hollow conducting sphere.
The charge on the outer surface of the hollow conducting sphere is the difference of the net charge and the charge at the inner surface. Thus, the total charge on the outer surface of the hollow conducting sphere.
[tex]=3.426\times 10^{-9}-1.791\times 10^{-9}\\=1.635\times 10^{-9}\\[/tex]
Hence, the total charge on the outer surface of the hollow conducting sphere is [tex]1.635\times 10^{-9}\\[/tex]
Hence,
- The charge on the insulating sphere is [tex]-1.791\times 10^{-9}[/tex] C.
- The net charge on the conducting sphere is [tex]3.426\times 10^{-9}[/tex] C.
- Total charge on the inner surface of the hollow conducting sphere is [tex]1.791\times 10^{-9}[/tex] C.
- The total charge on the outer surface of the hollow conducting sphere is [tex]1.635\times 10^{-9}\\[/tex]
Learn more about the electric field here;
https://brainly.com/question/12757739
