Правка разделов «Solution», «Answer»

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правка #18584 предыдущая #18583 ← раньше позже →
@@ -13,21 +13,25 @@Solution
Let's take a Gaussian sphere centered at the ball's center with radius $R$, and consider the differential form of Gauss law,\
$\vec{E}\cdot d\vec{S} = \frac{dq}{\varepsilon_0}$\
$\sigma = \frac{dq}{dS} = \varepsilon_0 E(R)$\
−but E(R) has a constant value independently on cavity position inside the ball. So, $\sigma$ is constant (the distribution over the outer surface is uniform).\
+but E(R) has a constant value independently on cavity position inside the ball. So, $\sigma$ is constant (**the distribution over the outer surface is uniform**).\
\
−Applying Gauss law for a Gaussian sphere of radius $R$ centered at the ball (total charge = Q'-Q' = 0),
−$\int\vec{E}\cdot d\vec{S} = \frac{-Q'+Q'+Q}{\varepsilon_0} = \frac{Q}{\varepslion_0}$ (1)\
+Applying Gauss law for a Gaussian sphere of radius $R$ centered at the ball (total charge = $Q'-Q'$ = 0),
+$\int\vec{E}\cdot d\vec{S} = \frac{-Q'+Q'+Q}{\varepsilon_0} = \frac{Q}{\varepsilon_0}$ (1)\
$\sigma = \frac{dq}{dS} = \varepsilon_0 E(R)$ (2)\
From (1),\
$E(R) = \frac{Q}{4\pi\varepsilon_0 R^2}$ (3)\
Putting (3) into (2),\
−$\sigma = \frac{Q}{4\pi R}$\
+$\sigma = \frac{Q}{4\pi R^2}$\
\
−Applying Gauss law for a sphere centered at ball and radius $r > R$,\
+Applying Gauss law for a sphere centered at ball and radius $r > R$ and evaluating at $r=L$,\
$\int \vec{E}\cdot d\vec{S} = \frac{q+Q}{\varepsilon_0}$\
$E(L) = \frac{q+Q}{4\pi\varepsilon_0 L^2}$\
−The value of E(L) doesn't depend on the cavity's position nor size of sphere, but the enclosed charge.
+The value of E(L) **doesn't depend on the cavity's position nor size of sphere, but the enclosed charge**.
#### Answer
−[Insert a concise answer or boxed result]
+$Q' = -Q$\
+Charge distribution obver the outer surface is uniform\
+$\sigma = \frac{Q}{4\pi R^2}$\
+$E(L) = \frac{q+Q}{4\pi\varepsilon_0 L^2}$\
+NO, NO