Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 21: Electric Charge and Electric Field

Problem 9a

Chapter 21, Problem 9a

Two small plastic spheres are given positive electric charges. When they are $15.0$ cm apart, the repulsive force between them has magnitude $0.220$ N. What is the charge on each sphere if the two charges are equal?

Verified step by step guidance

Start by identifying the formula for the electric force between two point charges, which is given by Coulomb's Law:

F = \frac{k q_{1} q_{2}}{r^{2}}

, where

F

is the force,

k

is Coulomb's constant (

8.99 \times 10 9^{N m^{2} C^{- 2}}

q_{1}

and

q_{2}

are the charges, and

r

is the distance between the charges.

Since the problem states that the two charges are equal, we can set

q_{1}

q_{2}

q

. Substitute this into Coulomb's Law to get:

F = \frac{k q^{2}}{r^{2}}

Rearrange the formula to solve for

q^{2}

q^{2} = \frac{F r^{2}}{k}

. Then, take the square root of both sides to find

q

q = \sqrt{\frac{F r^{2}}{k}}

Substitute the given values into the equation:

F

= 0.220 N,

r

= 0.15 m, and

k

8.99 \times 10 9^{N m^{2} C^{- 2}}

. Plug these values into the formula to find

q

Calculate the expression to find the charge

q

on each sphere. Remember to keep track of units and ensure they are consistent throughout the calculation.

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Key Concepts

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

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force 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. The formula is F = k * |q1 * q2| / r^2, where k is Coulomb's constant.

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, and like charges repel each other while opposite charges attract. In this problem, both spheres have positive charges, leading to a repulsive force between them.

Equilibrium of Forces

In physics, equilibrium refers to a state where all forces acting on an object are balanced, resulting in no net force and no acceleration. For the spheres, the repulsive force due to their charges must be equal and opposite to any other forces acting on them, ensuring they remain stationary or move uniformly.

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05:10

Equilibrium

Related Practice

Textbook Question

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. How many electrons does each sphere contain? (The atomic mass of aluminum is $26.982$ g/mol, and its atomic number is $13$ .)

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Textbook Question

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. What fraction of all the electrons in each sphere does this represent?

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Textbook Question

Three point charges are arranged on a line. Charge $q sub 3 equals positive 5.00$ nC and is at the origin. Charge $q_{2} = - 3.00$ nC and is at $x equals positive 4.00$ cm. Charge $q sub 1$ is at $x equals positive 2.00$ cm. What is $q sub 1$ (magnitude and sign) if the net force on $q sub 3$ is zero?

Textbook Question

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude $1.00 \times 10^{4}$ N (roughly $1$ ton)? Assume that the spheres may be treated as point charges.

Textbook Question

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4$\times$10^{-15}$ m. What magnitude of electric field does it produce at the distance of the electrons, which is about $1.0 \times 10^{- 10}$ m?

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Textbook Question

Two small plastic spheres are given positive electric charges. When they are $15.0$ cm apart, the repulsive force between them has magnitude $0.220$ N. What is the charge on each sphere if one sphere has four times the charge of the other?

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Two small plastic spheres are given positive electric charges. When they are 15.015.0 cm apart, the repulsive force between them has magnitude 0.2200.220 N. What is the charge on each sphere if the two charges are equal?

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Key Concepts

Coulomb's Law

Electric Charge

Equilibrium of Forces

Two small plastic spheres are given positive electric charges. When they are $15.0$ cm apart, the repulsive force between them has magnitude $0.220$ N. What is the charge on each sphere if the two charges are equal?