Two large rectangular aluminum plates of area 160 cm2 face each other with a separation of 3 mm between them. The plates are charged with equal amount of opposite charges, ±21 µC. The charges on the plates face each other. Find the flux (in N · m2/C) through a circle of radius 2.9 cm between the plates when the normal to the circle makes an angle of 9° with a line perpendicular to the plates. Note that this angle can also be given as 180° + 9°.

Φ=3.868×10⁵N.m²/C

Explanation:

Charge of plate q=21 µC =21×10⁻⁶C

Area of plate A₁=160 cm²=160×10⁻⁴m²

Permitivity of free space ε₀=8.85×10⁻¹²C²/N.m²

Area for calculating flux is given as:

Angle between the normal of the area and the electric field:θ=9°

The Charge density on the plate is given as:

σ=q/A₁

σ=21×10⁻⁶C/160×10⁻⁴m²

σ=1.3125×10⁻³C/m²

Electric field of an infinite oppositely charged parallel plates:

E=σ/ε₀

E=1.3125×10⁻³ / 8.85×10⁻¹²

E=1.483×10⁸N/C

The Electric flux for uniform electric field:

Φ=EACosΘ

Φ=1.483×10⁸(2.64074×10⁻³m²)Cos(9⁰)

Φ=3.868×10⁵N.m²/C

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