Question

Let the whole xy planet (z = 0) have charge density σ1 = 10 nC / m2 and the entire xz plane (y = 0) have charge density σ2 = -10 nC / m2.
Find the electric field (vector) in the points
a) (x, y, z) = (1,1,1) m
b) (x, y, z) = (-1, -1, -1) m

Answer 1

Answer on Question #81738, Physics / Electromagnetism

**Question:**

Let the whole xy planet (z = 0) have charge density σ1 = 10 nC / m2 and the entire xz plane (y = 0) have charge density σ2 = -10 nC / m2.

Find the electric field (vector) in the points

a) (x, y, z) = (1, 1, 1) m

b) (x, y, z) = (-1, -1, -1) m

**Solution:**

According to Gauss’s theorem for a plane $\overline{E_1} = \overline{k} 4\pi K\sigma_1 = \overline{k} 4\cdot 3.14\cdot 90 = \overline{k} 1.13(\frac{kV}{m})$ and $\overline{E_2} = \overline{j} 4\pi k\sigma_2 = -\overline{j} 1.13(\frac{kV}{m})$, therefore the net electric field vector at any point equals to

$$\overline{E} = 1.13(\overline{k} - \overline{j})\frac{kV}{m}.$$

**The answer:**

The net electric field vector at any point equals to $\overline{E} = 1.13(\overline{k} - \overline{j})\frac{kV}{m}$.

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