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 67

Chapter 25, Problem 67

FIGURE P25.67 shows two uniformly charged spheres. What is the potential difference between points 1 and 2? Which point is at the higher potential? Hint: The potential at any point is the superposition of the potentials due to all charges.

Verified step by step guidance

Step 1: Understand the concept of electric potential. The electric potential at a point due to a charge is given by the formula V = (k * Q) / r, where k is Coulomb's constant (8.99 × 10^9 N·m²/C²), Q is the charge, and r is the distance from the charge to the point.

Step 2: Calculate the potential at point 1 due to the 100 nC sphere. Use the formula V = (k * Q) / r, where Q = 100 nC and r is the radius of the sphere (30 cm or 0.3 m).

Step 3: Calculate the potential at point 1 due to the 25 nC sphere. Use the formula V = (k * Q) / r, where Q = 25 nC and r is the distance between point 1 and the center of the 25 nC sphere (100 cm or 1 m).

Step 4: Calculate the potential at point 2 due to the 100 nC sphere. Use the formula V = (k * Q) / r, where Q = 100 nC and r is the distance between point 2 and the center of the 100 nC sphere (100 cm or 1 m).

Step 5: Calculate the potential at point 2 due to the 25 nC sphere. Use the formula V = (k * Q) / r, where Q = 25 nC and r is the radius of the sphere (10 cm or 0.1 m). Add the potentials at each point to find the total potential at points 1 and 2, then subtract to find the potential difference. Compare the values to determine which point is at the higher potential.

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Key Concepts

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

Electric Potential

Electric potential at a point in space is the amount of electric potential energy per unit charge that a positive test charge would have at that point. It is influenced by the presence of electric charges and is measured in volts (V). The potential due to a point charge can be calculated using the formula V = kQ/r, where k is Coulomb's constant, Q is the charge, and r is the distance from the charge.

Superposition Principle

The superposition principle states that the total electric potential at a point due to multiple charges is the algebraic sum of the potentials due to each charge individually. This means that to find the potential at a point, one can calculate the potential from each charge separately and then add them together, taking into account their signs and distances.

Potential Difference

Potential difference, or voltage, between two points is defined as the difference in electric potential between those points. It indicates how much work is needed to move a unit charge from one point to another. In this context, determining which point has a higher potential involves comparing the calculated potentials at points 1 and 2, allowing us to ascertain the direction of electric force on a positive test charge.

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Potential Difference Between Two Charges

Related Practice

Textbook Question

Two metal objects that are in contact must be at the same potential, an assertion we'll prove in the next chapter. Suppose a metal sphere of radius R is charged to 1000 V and a second metal sphere of radius 2R is charged to 2000 V. The two spheres are brought into contact and then separated. Afterward, what is the potential of each sphere?

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Textbook Question

Two spherical drops of mercury each have a charge of 0.10 nC and a potential of 300 V at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

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Textbook Question

FIGURE P25.72 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center.

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Textbook Question

FIGURE P25.70 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.

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Textbook Question

The potential 1.0 cm from the surface of a metal sphere is 8000 V. The potential 3.0 cm from the surface is 4000 V. What is the radius of the sphere?

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Textbook Question

A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. What is the electric field strength just outside the surface of the sphere when it is charged to 500,000 V?

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