Ch 22: Electric Charges and Forces

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 22: Electric Charges and Forces

Problem 14a

Chapter 22, Problem 14a

Two small plastic spheres each have a mass of 2.0 g and a charge of −50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere?

Verified step by step guidance

Convert the given quantities into SI units: mass = 2.0 g = 0.002 kg, charge = -50.0 nC = -50.0 × 10⁻⁹ C, and distance = 2.0 cm = 0.02 m.

Recall Coulomb's Law, which gives the magnitude of the electric force between two charges:

F = \frac{| k_{e} | q_{1} q_{2}}{r^{2}}

, where

k_{e}

is Coulomb's constant (8.99 × 10⁹ N·m²/C²),

q_{1}

and

q_{2}

are the charges, and

r

is the distance between them.

Substitute the values into Coulomb's Law formula:

F = \frac{| (8.99 \times 10^{9}) (- 50.0 \times 10^{-9}) (- 50.0 \times 10^{-9}) |}{(^{0.02) 2}}

Simplify the numerator by multiplying the constants and charges, and simplify the denominator by squaring the distance. Ensure to handle the absolute value of the charges correctly, as the force is always positive in magnitude.

After simplifying, the result will give the magnitude of the electric force

F

in newtons (N).

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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 electrostatic force between two charged objects. It states that the force (F) is directly proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The formula is F = k * |q1 * q2| / r², where k is Coulomb's constant. This law is fundamental for calculating the electric force in this scenario.

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 while opposite charges attract. In this question, the spheres have a negative charge of -50.0 nC, which influences the nature of the force between them according to Coulomb's Law.

Distance in Electric Force Calculations

The distance between charged objects is crucial in determining the electric force acting between them. In Coulomb's Law, the force decreases with the square of the distance, meaning that even small changes in distance can significantly affect the force. In this case, the spheres are 2.0 cm apart, and this distance will be used in the calculations to find the magnitude of the electric force.

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Work due to Electric Force

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