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25. Electric Potential

Electric Potential

Physics

25. Electric Potential

Electric Potential

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Problem 36b

Textbook Question

Two point charges qₐ and qᵦ are located on the x-axis at x=a and x=b. FIGURE EX25.36 is a graph of V, the electric potential. What is the ratio |qₐ/qᵦ|?

Verified step by step guidance

Step 1: Understand the relationship between electric potential (V) and point charges. The electric potential due to a point charge q at a distance r is given by V = k * q / r, where k is Coulomb's constant.

Step 2: Analyze the graph provided. The graph shows two peaks at x = a and x = b, corresponding to the locations of the charges qₐ and qᵦ. The height of each peak represents the magnitude of the electric potential at those points.

Step 3: Note that the electric potential is proportional to the magnitude of the charge. The ratio of the heights of the peaks on the graph corresponds to the ratio of the magnitudes of the charges |qₐ| and |qᵦ|.

Step 4: Measure or compare the heights of the peaks at x = a and x = b from the graph. Let the height of the peak at x = a be Vₐ and the height of the peak at x = b be Vᵦ.

Step 5: Calculate the ratio |qₐ/qᵦ| using the proportionality between the electric potential and the charge. The ratio is given by |qₐ/qᵦ| = Vₐ / Vᵦ.

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Key Concepts

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

Electric Potential (V)

Electric potential, denoted as V, is the amount of electric potential energy per unit charge at a point in an electric field. It is a scalar quantity that indicates the work done to move a charge from a reference point to a specific point in the field without any acceleration. The shape of the graph in the question shows how the potential varies along the x-axis due to the influence of the point charges.

Point Charges

Point charges are idealized charges that are considered to be concentrated at a single point in space. They create electric fields and potentials around them, which can be analyzed using Coulomb's law. In this scenario, the charges qₐ and qᵦ at positions a and b affect the electric potential V along the x-axis, and their magnitudes and signs determine the shape of the potential graph.

Ratio of Charges

The ratio of charges |qₐ/qᵦ| is a dimensionless quantity that compares the magnitudes of two point charges. This ratio can be derived from the electric potential at specific points in the field created by these charges. Understanding this ratio is crucial for solving the problem, as it relates the strengths of the electric potentials at points a and b to the respective charges.

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Textbook Question

What is the electric potential at the point indicated with the dot in FIGURE EX25.31?

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A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?

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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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Which point in FIGURE EX26.5, A or B, has a larger electric potential?

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The electric field in a region of space is E_x=5000x V/m , where x is in meters. Find an expression for the potential V at position x. As a reference, let V=0 V at the origin.

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An electric dipole at the origin consists of two charges ±q spaced distance s apart along the y-axis. Find an expression for the potential V(x, y) at an arbitrary point in the xy-plane. Your answer will be in terms of q, s, x, and y.

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