Math Problem Statement

Calculate the electrostatic force between the two charges in the figure below.

Solution

Problem 1: Calculate the Electrostatic Force Between the Two Charges

Given:

  • Charge at point A, qA=+2.4μCq_A = +2.4 \, \mu C
  • Charge at point B, qB=+3.6μCq_B = +3.6 \, \mu C
  • Distance between the charges, r=20cm=0.20mr = 20 \, \text{cm} = 0.20 \, \text{m}

The electrostatic force between two charges is calculated using Coulomb's law:

F=keqAqBr2F = k_e \cdot \frac{|q_A \cdot q_B|}{r^2}

where:

  • kek_e is Coulomb's constant, ke=8.99×109Nm2/C2k_e = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2
  • qAq_A and qBq_B are the magnitudes of the charges
  • rr is the distance between the charges

Substituting the given values:

F=8.99×1092.4×1063.6×106(0.20)2F = 8.99 \times 10^9 \cdot \frac{|2.4 \times 10^{-6} \cdot 3.6 \times 10^{-6}|}{(0.20)^2}

F=8.99×1098.64×10120.04F = 8.99 \times 10^9 \cdot \frac{8.64 \times 10^{-12}}{0.04}

F=8.99×1092.16×1010F = 8.99 \times 10^9 \cdot 2.16 \times 10^{-10}

F=1.94×109NF = 1.94 \times 10^{-9} \, \text{N}

So, the electrostatic force between the two charges is approximately 1.94N**1.94 \, \text{N}**.

Problem 2: Calculate the Net Electrostatic Force on the Charge (A)

For the second problem, I need to analyze the additional diagram to understand the configuration of charges and their respective distances from charge A. Since this part isn't fully visible in the current image, please provide more details or a clearer image for accurate calculation.

Do you want to proceed with the net force calculation or have any specific questions?

Related Questions:

  1. What happens to the force if the distance between the charges is halved?
  2. How would the force change if one of the charges was negative?
  3. What is the physical significance of the direction of the electrostatic force?
  4. How does the principle of superposition apply to calculating the net force on charge A?
  5. How does Coulomb's law compare to Newton's law of universal gravitation?

Tip: Remember that electrostatic forces between like charges are repulsive, while forces between opposite charges are attractive.

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Math Problem Analysis

Mathematical Concepts

Electrostatics
Coulomb's Law

Formulas

F = k_e * |q_A * q_B| / r^2

Theorems

Coulomb's Law

Suitable Grade Level

Grade 12