Two point charges, [math: q1=+7μC] and [math: q2=−7μC] , are placed 0.21 m apart in a vacuum. What is the magnitude of the net electric field, at the midpoint between the two charges?*Note: [math: 1.23×104NC−1] is written as 1.23e4 N/C

Question

Two point charges, [math: q1=+7μC] and [math: q2=−7μC] , are placed 0.21 m apart in a vacuum. What is the magnitude of the net electric field, at the midpoint between the two charges?*Note: [math: 1.23×104NC−1] is written as 1.23e4 N/C

BlackTom AI · Accepted Answer

Electric field from a point charge is E = k|q|/r^2, so use Coulomb’s law and superposition. Here k = 8.988×10^9 N·m^2/C^2, q1 = +7.0×10^−6 C, q2 = −7.0×10^−6 C, separation d = 0.21 m. The midpoint is r = d/2 = 0.105 m from each charge.

Step-by-step calculation:
1. Distance squared: r^2 = (0.105 m)^2 = 0.011025 m^2.
2. Magnitude of the field from one charge:
   E_single = k|q|/r^2
            = (8.988×10^9 N·m^2/C^2)(7.0×10^−6 C) / 0.011025 m^2.
   Multiply numerator: 8.988×10^9 × 7.0×10^−6 = (8.988×7.0)×10^3 = 62.916×10^3 = 6.2916×10^4.
   Divide by r^2: E_single = 6.2916×10^4 / 0.011025 ≈ 5.7066×10^6 N/C.
3. Direction and superposition: The positive charge produces a field pointing away from it; the negative charge produces a field pointing toward it. At the midpoint the two fields point in the same direction (from + toward −), so magnitudes add.
4. Total field magnitude: E_net = 2 × E_single ≈ 2 × 5.7066×10^6 N/C ≈ 1.1413×10^7 N/C ≈ 1.14e7 N/C.

Why this option is correct:
- The calculation uses correct Coulomb constant, correct distances, and correctly adds the two equal-magnitude fields because their directions at the midpoint coincide. That yields 1.14×10^7 N/C, matching choice c.

Why other options are incorrect:
- (a) 2.85e6 N/C is about half of E_single (incorrect superposition or wrong r).
- (b) 2.85e12 N/C is many orders of magnitude too large (numerical error).
- (d) 5.71e6 N/C equals the field from one charge only, not the net from both.

Conclusion: The net electric field at the midpoint is 1.14e7 N/C, confirming answer c.

Two point charges, [math: q1=+7μC] and [math: q2=−7μC] , are placed 0.21 m apart in a vacuum. What is the magnitude of the net electric field, at the midpoint between the two charges?*Note: [math: 1.23×104NC−1] is written as 1.23e4 N/C单项选择题

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