An electric field, E = (2î + 6ĵ + 8k̂)/√6 passes through the surface of 4 m² area having unit vector n̂ = (2î + ĵ + k̂)/√6. The electric flux for that surface i s _________ V m.
Physics · Electrostatics · electric flux and gauss law
JEE Mains 2024 08 Apr Morning Shift

Question

An electric field, E = (2î + 6ĵ + 8k̂)/√6 passes through the surface of 4 m² area having unit vector n̂ = (2î + ĵ + k̂)/√6. The electric flux for that surface i s _________ V m.

G1 Physics · Accepted Answer

Electric flux: Φ = E · A Area vector: A = 4n̂ Therefore: Φ = [(2î + 6ĵ + 8k̂)/√6] · [4(2î + ĵ + k̂)/√6] = (4/6)(4 + 6 + 8) = (4/6)(18) = 12 V m