If point A is between the two charges. And charge q1 is 5cm from A and q2 is 15cm from A on the opposite side, what’s the net Electric Field on A

Physics

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Answer

Enet≈3.196×1012q N/C\text{E}_{net} \approx 3.196 \times 10^{12} q \text{ N/C}

Step-by-step solution

5 steps

To find the net electric field at point A, we need to calculate the electric field due to each charge individually and then sum them vectorially. We'll assume both charges have the same positive magnitude, qq.

  1. Identify given distances and constants.

    The distance from charge q1q_1 to point A is r1=5 cm=0.05 mr_1 = 5 \text{ cm} = 0.05 \text{ m}.
    The distance from charge q2q_2 to point A is r2=15 cm=0.15 mr_2 = 15 \text{ cm} = 0.15 \text{ m}.
    Let the magnitude of both charges be qq.
    Coulomb's constant is k=8.987×109 N⋅m2/C2k = 8.987 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2.
    The formula for the electric field due to a point charge is E=kqr2E = \frac{kq}{r^2}.

  2. Determine the direction of the electric fields at point A.

    Assume q1q_1 and q2q_2 are both positive charges. Let q1q_1 be to the left of A and q2q_2 be to the right of A.

    • The electric field E1E_1 due to q1q_1 at A points away from q1q_1 (to the right).
    • The electric field E2E_2 due to q2q_2 at A points away from q2q_2 (to the left).
  3. Calculate the magnitudes of E1E_1 and E2E_2.

    E1=kq1r12=kq(0.05 m)2=kq0.0025 m2=400kq N/CE_1 = \frac{k q_1}{r_1^2} = \frac{k q}{(0.05 \text{ m})^2} = \frac{k q}{0.0025 \text{ m}^2} = 400 k q \text{ N/C} E2=kq2r22=kq(0.15 m)2=kq0.0225 m2≈44.44kq N/CE_2 = \frac{k q_2}{r_2^2} = \frac{k q}{(0.15 \text{ m})^2} = \frac{k q}{0.0225 \text{ m}^2} \approx 44.44 k q \text{ N/C}
  4. Calculate the net electric field at point A.

    Since E1E_1 points to the right and E2E_2 points to the left, and E1E_1 is larger than E2E_2, the net electric field will point to the right.

    Enet=E1−E2E_{net} = E_1 - E_2 Enet=400kq−44.44kqE_{net} = 400 k q - 44.44 k q Enet=(400−44.44)kqE_{net} = (400 - 44.44) k q Enet=355.56kq N/CE_{net} = 355.56 k q \text{ N/C}
  5. Substitute the value of kk and state the final answer.

    Enet=355.56×(8.987×109 N⋅m2/C2)×qE_{net} = 355.56 \times (8.987 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2) \times q Enet≈3.196×1012q N/CE_{net} \approx 3.196 \times 10^{12} q \text{ N/C}

    The net electric field at point A is approximately 3.196×1012q N/C3.196 \times 10^{12} q \text{ N/C} and points towards the charge q2q_2 (or away from q1q_1). The exact numerical value depends on the magnitude of the charge qq.

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