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Two square, parallel conducting plates each have dimensions 5.00 cm by 5.00 cm and are placed 0.100 mm apart. They are charged with +20 nC and -20 nC, respectively.

What is the electric field between the plates? Calculate the magnitude and indicate the direction of the electric field.

Answer :

Final answer:

The electric field between two parallel conducting plates with charges of +20nC and -20nC, separated by 0.100 mm, is 9.04 × 106 N/C, directed from the positive plate to the negative plate.

Explanation:

Calculation of Electric Field Between Parallel Plates

To calculate the electric field between two parallel conducting plates, we use the formula E = σ/ε0, where σ is the surface charge density, and ε0 is the permittivity of free space (ε0 = 8.85 × 10−12 C2/N·m2). In this case, each plate has dimensions 5.00 cm by 5.00 cm and they are charged +20nC and -20nC respectively.

The area A of each plate is (5.00 cm × 5.00 cm) converted to square meters. The surface charge density σ can be found by σ = Q/A, where Q is the charge on the plates. Finally, using the formula for the electric field, we get the magnitude E.

The charge density σ is given by:

σ = 20 × 10−9 C / (0.05 m × 0.05 m)

= 8 × 10−6 C/m2.

Thus, the electric field E is:

E = σ/ε0 = (8 × 10−6 C/m2) / (8.85 × 10−12 C2/N·m2)

= 9.04 × 106 N/C.

The direction of the electric field is from the positively charged plate to the negatively charged plate.

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