91影视

The scale of the vertical axis, ${\mathrm{蠒}}_{\mathrm{s}}=5.0脳{10}^5\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}$

Using the concept of the Gauss law, we can get the charge enclosed by the surface. This value of the enclosed charge will determine the charge of the shells of A and B.

Formula:

The enclosed charge by the surface, ${\mathrm{q}}_{\mathrm{enc}}={\mathrm{蔚}}_0\mathrm{蠒}$ (1)

From the graph, the value ${\mathrm{蠒}}_{\mathrm{s}}=2.0脳{10}^5{\mathrm{Nm}}^2/\mathrm{C}$for small r leads to the charge of the central particle using equation (1i) as:

$$\begin{gathered} {\mathrm{q}}_{\mathrm{centre}}=(8.85脳{10}^{-12}{\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2)(2.0脳{10}^5\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}) \\ =1.77脳{10}^{-6}\mathrm{C} \end{gathered}$$

Hence, the value of the charge is $1.77脳{10}^{-6}\mathrm{C}$.

The next value that takes the flux is given as:

${\mathrm{蠒}}_{\mathrm{s}}=-4.0脳{10}^5\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}$

which implies that the charge enclosed by it using equation (1) is given as:

${\mathrm{q}}_{\mathrm{enc}}=-3.54脳{10}^{-6}\mathrm{C}$

But we have already accounted for some of that charge in part (a), so the result for part (b) is calculated as follows:

$$\begin{gathered} {\mathrm{q}}_{\mathrm{A}}={\mathrm{q}}_{\mathrm{enc}}-{\mathrm{q}}_{\mathrm{centre}} \\ =-5.3脳{10}^{-6}\mathrm{C} \end{gathered}$$

Hence, the value of the charge is $-5.3脳{10}^{-6}\mathrm{C}$.

Finally, for the large r-value, the value of the flux is given as:

$\mathrm{蠒}=6.0脳{10}^5\mathrm{N}.{\mathrm{m}}^2/\mathrm{C}$

which implies that the enclosed charge for this flux value is given using equation (1) as:

role="math" localid="1657346976925" ${\mathrm{q}}_{\mathrm{totalence}}=5.31脳{10}^{-6}\mathrm{C}$

Considering what we have already found, then the result of the charge of the shell is given as:

$$\begin{gathered} {\mathrm{q}}_{\mathrm{B}}={\mathrm{q}}_{\mathrm{total}\mathrm{enc}}-{\mathrm{q}}_{\mathrm{A}}={\mathrm{q}}_{\mathrm{centre}} \\ =+8.9\mathrm{渭颁} \end{gathered}$$

Hence, the value of the charge is $+8.9\mathrm{渭颁}$.