Question

Two flat 4.0 cm × 4.0 cm electrodes carrying equal but opposite charges are spaced 2.0 mm apart with their midpoints opposite each other. between the electrodes but not near their edges, the electric field strength is 6.8 × 106 n/c. what is the magnitude of the charge on each electrode? (ε 0 = 8.85 × 10-12 c2/n · m2)

Answer 1

Answer:

$9.5 \cdot 10^{-8} C$

Explanation:

The electric field between two charged plates is uniform, and its strength is given by

$E=\frac{\sigma}{\epsilon_0}$

where

$\sigma=\frac{Q}{A}$ is the charge density, with Q being the charge on one plate and A the area of the plate

$\epsilon_0=8.85 \cdot 10^{-12} C^ N^{-1} m^{-2}$ is the dielectric constant

Since we know the magnitude of the field, $E=6.8 \cdot 10^6 N/C$, we can find the charge density:

$\sigma=\epsilon_0 E=(8.85 \cdot 10^{-12})(6.8 \cdot 10^6 )=6.0 \cdot 10^{-5} C m^{-2}$

The area of each plate is

$A=(0.04 m)^2=1.6 \cdot 10^{-3} m^2$

So the charge on each electrode is

$Q=\sigma A=(6.0 \cdot 10^{-5})(1.6 \cdot 10^{-3})=9.5 \cdot 10^{-8} C$