An electric field, E⃗=(2 î+6 ĵ+8 k̂)/√6 passes through the surface of 4 m² area having unit vector n=((2 î+ĵ+k̂)/√6). The electric flux for that surface is _________ Vm.

Solution

Physics sir · 3 steps

Flux is just E⃗·n times the area, so take the dot product first, then scale by 4.

1. Area vector. For a flat surface the area vector is the area times the unit normal: A⃗ = 4 n. The flux is φ = E⃗·A⃗ = (E⃗·n) A.

   E⃗·n = ((2)(2) + (6)(1) + (8)(1))/(√6×√6) = 18/6 = 3 V m⁻¹

2. Multiply by area. φ = 3 × 4 = 12 V m.
3. So. The electric flux through the surface is 12 V m.

The common slip: 3. Stopping at E⃗·n gives 3, which is the field component along the normal, not the flux. Multiply by the 4 m² area.

The idea to keep. For a uniform field through a flat surface, φ = (E⃗·n)A. Watch the √6 in both vectors: together they give 6, not √6.

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