The electric field in a region is given E = ((3)/(5) î + (4)/(5) ĵ) N/C. The ratio of flux of reported field through the rectangular surface of area 0.2 m² (parallel to y-z plane) to that of surface of area 0.3 m² (parallel to x-z plane) is a: b, where a = _____. [Here, î, ĵ and k̂ are

Question

The electric field in a region is given E = ((3)/(5) î + (4)/(5) ĵ) N/C. The ratio of flux of reported field through the rectangular surface of area 0.2 m² (parallel to y-z plane) to that of surface of area 0.3 m² (parallel to x-z plane) is a: b, where a = _____. [Here, î, ĵ and k̂ are unit vectors along x, y and z-axes respectively]

Accepted Answer

3. The electric flux through a surface is given by the product of the electric field and the area of the surface projected in the direction of the field. For the rectangular surface parallel to the y-z plane, the area is 0.2 m² and the electric field has a component of rac{4}{5} N/C in the j direction, resulting in a flux of 0.2 * rac{4}{5} = 0.16 N·m²/C. For the surface parallel to the x-z plane, the area is 0.3 m² and the electric field has a component of rac{3}{5} N/C in the i direction, resulting in a flux of 0.3 * rac{3}{5} = 0.18 N·m²/C. The ratio of these two fluxes is 0.16:0.18, which simplifies to 3:5, thus a = 3.

Solution

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