If the electric field is given by E = 6î + 3ĵ + 4k̂, calculate the ...

Question

If the electric field is given by E = 6î + 3ĵ + 4k̂, calculate the electric flux through a surface of area 20 units lying in the yz-plane.

Accepted Answer

Given:
• Electric field: E = 6î + 3ĵ + 4k̂
• Surface area = 20 units
• Surface lies in the yz-plane

Step 1: Identify the area vector
Since the surface lies in the yz-plane, its normal is along the x-axis.

Area vector: A = 20 î

Step 2: Apply formula for electric flux
φ = E · A (dot product)

Step 3: Calculate dot product
φ = (6î + 3ĵ + 4k̂) · (20 î)

φ = (6 × 20) + (3 × 0) + (4 × 0)

φ = 120 + 0 + 0

φ = 120 units

Final Answer:
Electric flux through the surface = 120 N·m²/C (or 120 in given units)

Note: Only the x-component of E contributes to the flux, since the area vector is along x-axis.

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