Ch 25: The Electric Potential

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 25: The Electric Potential

Problem 5

Chapter 25, Problem 5

What is the electric potential energy of the group of charges in FIGURE EX25.5?

Verified step by step guidance

Step 1: Understand the concept of electric potential energy. The electric potential energy of a system of charges is calculated using the formula: U = k * (q1 * q2) / r, where k is Coulomb's constant (8.99 × 10^9 N·m²/C²), q1 and q2 are the charges, and r is the distance between them.

Step 2: Identify the charges and distances in the figure. The charges are: +1.0 nC, +1.0 nC, and -2.0 nC. The distances between the charges are all 3.0 cm (0.03 m).

Step 3: Calculate the potential energy for each pair of charges. There are three pairs: (1) +1.0 nC and +1.0 nC, (2) +1.0 nC and -2.0 nC, and (3) +1.0 nC and -2.0 nC. Use the formula U = k * (q1 * q2) / r for each pair.

Step 4: Add the potential energies of all pairs to find the total electric potential energy of the system. Since potential energy is scalar, simply sum the values obtained for each pair.

Step 5: Ensure units are consistent throughout the calculation. Convert charges to coulombs (1 nC = 1 × 10^-9 C) and distances to meters (3.0 cm = 0.03 m) before substituting into the formula.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. It is calculated based on the interaction between charges, where like charges repel and opposite charges attract. The formula for potential energy between two point charges is given by U = k * (q1 * q2) / r, where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force F between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating the forces acting on the charges in the given configuration, which is essential for determining the total electric potential energy.

Superposition Principle

The superposition principle in electrostatics states that the total electric potential energy of a system of charges is the sum of the potential energies of each pair of charges. This means that when calculating the potential energy for multiple charges, one can consider the interactions between each pair separately and then add them together. This principle simplifies the analysis of complex charge arrangements, such as the one presented in the question.

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Related Practice

Textbook Question

The electric field strength is 50,000 N/C inside a parallel-plate capacitor with a 2.0 mm spacing. A proton is released from rest at the positive plate. What is the proton's speed when it reaches the negative plate?

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Textbook Question

FIGURE EX25.10 shows the potential energy of an electric dipole. Consider a dipole that oscillates between ±60°. What is the dipole's mechanical energy?

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Textbook Question

Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 μJ, what is the magnitude of the force between the two charges?

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Textbook Question

Three charged particles are placed at the corners of an equilateral triangle that has edge length 2.0 cm. One particle has charge +3.0 nC and a second has charge +6.0 nC. What is the third charge if the electric potential energy of the three charged particles is zero?

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Textbook Question

An electron is released from rest at the center of a parallel-plate capacitor that has a 1.0 mm spacing. The electron then strikes one of the plates with a speed of 1.5×10⁶ m/s. What is the electric field strength inside the capacitor?

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