The magnitude and direction of the electric field in a particular region is (10 i +4 j +2 k ) 10^4 NC ⁻¹ . What s the electric flux through an area (3 i - k ) 10⁻² ~m ^2

Step-by-step solution

The electric flux _E through a surface is given by the dot product of the electric field vector E and the area vector A . Given E = (10 i + 4 j + 2 k ) 10^4 NC ⁻¹ and A = (3 i - k ) 10⁻² m ^2 . The flux is calculated as _E = E A . Substituting the vectors: _E = [(10 i + 4 j + 2 k ) 10^4] [(3 i + 0 j - 1 k ) 10⁻²] _E = (10^4 10⁻²) [(10 i + 4 j + 2 k ) (3 i + 0 j - 1 k )] _E = 10^2 [(10 3) + (4 0) + (2 -1)] _E = 100 [30 + 0 - 2] _E = 100 28 = 2800 Nm ^2 C ⁻¹ Expressing in scientific notation, _E = 2.8 10^3 Nm ^2 C ⁻¹