The electric field in a region is given by E⃗=(2 î+4 ĵ+6 k̂) × 10³ N / C. The flux of the field through a rectangular surface parallel to x-z plane is 6.0 Nm² C⁻¹. The area of the surface is _____________ cm².

Solution

Physics sir · 4 steps

A surface parallel to the x-z plane faces the y-direction, so only E_y sends flux through it.

1. Area vector. The area vector of a flat surface points along its normal. A surface parallel to the x-z plane has its normal along ĵ, so A⃗ = A ĵ.
2. Pick the component. Flux is φ = E⃗ · A⃗. The î and k̂ parts of E⃗ run along the surface and give zero. Only E_y = 4 × 10³ N C⁻¹ counts.

   φ = E_y A ⇒ A = 6.0/(4 × 10³) = 1.5 × 10⁻³ m²

3. Convert units. Since 1 m² = 10⁴ cm², the area is 1.5 × 10⁻³ × 10⁴ = 15 cm².
4. So. The area of the surface is 15 cm².

The common slip: 10. Taking the area vector along k̂ and using E_z = 6 × 10³ N C⁻¹ gives 10, not 15. The normal to the x-z plane is ĵ.

The idea to keep. A surface parallel to a plane has its area vector along the third axis. Parallel to x-z means along y, so only the y-component of the field gives flux.

Answer from the NTA final answer key. Solution by PrepWiser.