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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
All textbooksKnight Calc 5th EditionCh 25: The Electric PotentialProblem 38a
Chapter 25, Problem 38a

A −10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. What is the electric potential at the point on the x-axis where the electric field is zero?

Verified step by step guidance
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Step 1: Understand the problem. The electric field is zero at a point where the contributions from both charges cancel each other out. This point is not necessarily the midpoint between the charges because the magnitudes of the charges are different. Use the principle of superposition to find this point.
Step 2: Set up the equation for the electric field. The electric field due to a point charge is given by \( E = \frac{k \cdot q}{r^2} \), where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge. At the point where the electric field is zero, the magnitudes of the electric fields from both charges are equal: \( \frac{k \cdot q_1}{r_1^2} = \frac{k \cdot q_2}{r_2^2} \).
Step 3: Solve for the distance \( r_1 \) and \( r_2 \). Let \( r_1 \) be the distance from the −10.0 nC charge to the point where the electric field is zero, and \( r_2 \) be the distance from the +20.0 nC charge to the same point. Since the charges are 15.0 cm apart, \( r_1 + r_2 = 15.0 \, \text{cm} \). Substitute \( r_2 = 15.0 \, \text{cm} - r_1 \) into the equation from Step 2.
Step 4: Calculate the electric potential at the point where the electric field is zero. The electric potential due to a point charge is given by \( V = \frac{k \cdot q}{r} \). At the point where the electric field is zero, the potentials from both charges add algebraically: \( V = \frac{k \cdot q_1}{r_1} + \frac{k \cdot q_2}{r_2} \). Use the values of \( r_1 \) and \( r_2 \) found in Step 3 to calculate the potential.
Step 5: Verify the solution conceptually. Ensure that the electric field is indeed zero at the calculated point and that the electric potential is consistent with the principle of superposition. This step helps confirm the correctness of the approach and the calculations.

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Key Concepts

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

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charges can be positive or negative, with like charges repelling and opposite charges attracting each other. In this problem, we have a negative charge (-10.0 nC) and a positive charge (+20.0 nC), which will influence the electric field and potential in their vicinity.
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Electric Field

The electric field is a vector field that represents the force exerted by an electric charge on other charges in its vicinity. It is defined as the force per unit charge and points away from positive charges and towards negative charges. In this scenario, the electric field created by the two point charges will determine the location along the x-axis where the net electric field is zero, which is crucial for solving the problem.
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Electric Potential

Electric potential, often referred to as voltage, is the work done per unit charge in bringing a charge from infinity to a point in an electric field. It is a scalar quantity and can be calculated for point charges using the formula V = k * (q/r), where k is Coulomb's constant, q is the charge, and r is the distance from the charge. Understanding electric potential is essential for determining the potential at the point where the electric field is zero in this problem.
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Related Practice
Textbook Question

A +3.0 nC charge is at x=0 cm and a −1.0 nC charge is at x=4 cm. At what point or points on the x-axis is the electric potential zero?

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Textbook Question

A −3.0 nC charge is on the x-axis at x=−9 cm and a +4.0 nC charge is on the x-axis at x=16 cm. At what point or points on the y-axis is the electric potential zero?

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Textbook Question

Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.0 μC. What is the tension in the string?

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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. Draw a graph of Eₓ, the x-component of the electric field, as a function of x.

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Textbook Question

Two point charges 2.0 cm apart have an electric potential energy −180 μJ. The total charge is 30 nC. What are the two charges?

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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|?

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