Expression for an electric field is given by E⃗=4000 x² î V/m. The electric flux through the cube of side 20 cm when placed in electric field (as shown in the figure) is __________ V cm.

Solution

Physics sir · 4 steps

The field points only along x, so just two faces matter, and the one at x = 0 has zero field.

1. Which faces count. E⃗ has only an î component, so it runs parallel to the four faces normal to y and z. Those four faces get zero flux. Only the faces at x = 0 and x = 0.2 m remain.
2. Face at origin. On the face at x = 0, E = 4000 × 0² = 0. So this face gives no flux at all.
3. Far face. On the face at x = 0.2 m, E = 4000 × 0.2² = 160 V m⁻¹. It has this value everywhere on the face and points outward along +x. Multiply it by the face area 0.2² = 0.04 m².

   φ = E(0.2) A = 160 × 0.04 = 6.4 V m

4. So. Since 1 V m = 100 V cm, the net flux is 6.4 × 100 = 640 V cm.

The common slip: 6.4. Stopping at the SI result gives 6.4, which is in V m. The question asks for V cm, so multiply by 100.

The idea to keep. When a field points along one axis, only the faces normal to that axis carry flux. Find E on each of those faces, multiply by the area, and take outward minus inward.

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