Question Detail
Question
A circular ring 5 cm in radius has a positive charge of 3 x 10-7 C. Compute the magnitude of the electric field intensity on the axis of the ring 4 cm from its centre.
Correct Answer
Option D is the correct answer.
Detailed Explanation
The electric field intensity (E) on the axis of a uniformly charged ring at a distance x from its center is given by the formula:E = (k * Q * x) / (R2 + x2)3/2Given:Radius R = 5 cm = 0.05 mCharge Q = 3 × 10-7 CDistance x = 4 cm = 0.04 mCoulomb's constant k ≈ 8.9875 × 109 N·m2/C2Substitute the values:E = (8.9875 × 109 × 3 × 10-7 × 0.04) / ((0.05)2 + (0.04)2)3/2E = (1.0785 × 102) / (0.0025 + 0.0016)3/2E = (107.85) / (0.0041)3/2E = (107.85) / (0.0041 × √0.0041)E = (107.85) / (0.0041 × 0.06403)E = (107.85) / (0.000262523)E ≈ 410817 N/C ≈ 4.11 × 105 N/CThis is approximately 4.1 × 105 N/C.
Hint
Use the formula for the electric field on the axis of a charged ring. Ensure all units are consistent (e.g., meters for distances).