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.

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.