The electric field in a region is 𝐄 = 3y $\hat{j}.$ Find the total electrostatic energy stored in the electric field inside the cube of side a shown in the figure.
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The electric field in a region is 𝐄 = 3y j ^ . \hat{j}. j ^ ​ . Find the total electrostatic energy stored in the electric field inside the cube of side a shown in the figure.

G1 Physics · Accepted Answer

Step 1: Field-energy density is u=(1/2)ε₀E²=(1/2)ε₀(3y)²=(9/2)ε₀y². Step 2: For a cube 0≤x,y,z≤a, dV=dx dy dz, so U=(9/2)ε₀a²∫₀ᵃy²dy. Step 3: U=(9/2)ε₀a²(a³/3)=(3/2)ε₀a⁵. Final: C.

The electric field in a region is 𝐄 = 3y j ^ . \hat{j}. j ^ ​ . Find the total electrostatic energy stored in the electric field inside the cube of side a shown in the figure.

The electric field in a region is 𝐄 = 3y j ^ . \hat{j}. j ^ . Find the total electrostatic energy stored in the electric field inside the cube of side a shown in the figure.