An electric field E ⃗ \vec{E} E = E₀ i ^ \hat{i} i ^ + E₀ j ^ \hat{j} j ^ exists in space. Find the flux through a triangular loop with vertices (a/2, 0, 0), (a/2, 0, a) and (a/2, a, a/2).
Physics · Electrostatic
JEE Mains Advanced

Question

An electric field E ⃗ \vec{E} E = E₀ i ^ \hat{i} i ^ + E₀ j ^ \hat{j} j ^ ​ exists in space. Find the flux through a triangular loop with vertices (a/2, 0, 0), (a/2, 0, a) and (a/2, a, a/2).

G1 Physics · Accepted Answer

Step 1: All three vertices have x = a/2, so the triangular loop lies in a plane parallel to the yz-plane; its area vector is along ±𝐢. Step 2: Base = a and height = a, hence area = a²/2. Since Eₓ = E₀, |Φ| = E₀(a²/2). Final: B.

An electric field E ⃗ \vec{E} E = E₀ i ^ \hat{i} i ^ + E₀ j ^ \hat{j} j ^ ​ exists in space. Find the flux through a triangular loop with vertices (a/2, 0, 0), (a/2, 0, a) and (a/2, a, a/2).

An electric field E ⃗ \vec{E} E = E₀ i ^ \hat{i} i ^ + E₀ j ^ \hat{j} j ^ exists in space. Find the flux through a triangular loop with vertices (a/2, 0, 0), (a/2, 0, a) and (a/2, a, a/2).