An electric field given by 𝐄 = 4 i ^ \hat{i} i ^ -3(y² + 2) j ^ \hat{j} j ^ pierces Gaussian’s cube of side 1m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by -nε₀. Find the value of n.
Physics · Electrostatic · electric flux and gauss law
JEE Advanced

Question

An electric field given by 𝐄 = 4 i ^ \hat{i} i ^ -3(y² + 2) j ^ \hat{j} j ^ pierces Gaussian’s cube of side 1m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by -nε₀. Find the value of n.

Physics · Electrostatic · electric flux and gauss law

G1 Physics · Accepted Answer

Step 1: Choose a Gaussian surface consistent with the symmetry. Step 2: Apply ∮𝐄·d𝐀 = Q/ε₀; charges outside affect local E but do not contribute to Q. Step 3: Evaluate the enclosed charge from the given density/geometry and solve for the requested quantity. Final: 3.

An electric field given by 𝐄 = 4 i ^ \hat{i} i ^ -3(y² + 2) j ^ \hat{j} j ^ ​ pierces Gaussian’s cube of side 1m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by -nε₀. Find the value of n.

An electric field given by 𝐄 = 4 i ^ \hat{i} i ^ -3(y² + 2) j ^ \hat{j} j ^ pierces Gaussian’s cube of side 1m placed at origin such that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by -nε₀. Find the value of n.