An electric field is given by (6 î+5 ĵ+3 k̂) N / C. The electric flux through a surface area 30 î m² lying in YZ-plane (in SI unit) is :

Solution

Physics sir · 3 steps

Flux is a dot product, and an area vector along î only picks up the x-part of the field.

1. Area as a vector. A surface in the YZ-plane has its normal along the x-axis. So its area vector is A⃗ = 30î m², with no y or z part.

   φ = E⃗·A⃗ = (6î+5ĵ+3k̂)·(30î)

2. Only x survives. Since ĵ·î = 0 and k̂·î = 0, the 5ĵ and 3k̂ parts run along the surface and give no flux. Only 6 × 30 remains.
3. So. φ = 180 N m² C⁻¹, which is option (c).

The idea to keep. For a flat surface in a uniform field, write the area as a vector along its normal and take E⃗·A⃗. Field parts lying along the surface add no flux.

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