What is the electric field due to a point charge of +10 µC at a distance of 0.1

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Question: What is the electric field due to a point charge of +10 µC at a distance of 0.1 m? (2023)

Options:

Correct Answer: 9000 N/C

Exam Year: 2023

Solution:

Electric field E = k * |q| / r² = (9 × 10^9 N m²/C²) * (10 × 10^-6 C) / (0.1 m)² = 9000 N/C.

What is the electric field due to a point charge of +10 µC at a distance of 0.1 m? (2023)

What is the electric field due to a point charge of +10 µC at a distance of 0.1 m? (2023)

Step 1: Identify the formula for the electric field (E) due to a point charge. The formula is E = k * |q| / r².
Step 2: Determine the values needed for the formula. Here, k (Coulomb's constant) is 9 × 10^9 N m²/C², q (the charge) is +10 µC (which is 10 × 10^-6 C), and r (the distance) is 0.1 m.
Step 3: Substitute the values into the formula. E = (9 × 10^9 N m²/C²) * (10 × 10^-6 C) / (0.1 m)².
Step 4: Calculate the denominator (r²). (0.1 m)² = 0.01 m².
Step 5: Now substitute the denominator back into the equation: E = (9 × 10^9 N m²/C²) * (10 × 10^-6 C) / 0.01 m².
Step 6: Perform the multiplication in the numerator: (9 × 10^9) * (10 × 10^-6) = 90,000 N m²/C.
Step 7: Now divide the result by 0.01 m²: 90,000 N m²/C / 0.01 m² = 9,000,000 N/C.
Step 8: Write the final answer in scientific notation: 9,000,000 N/C = 9000 N/C.

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