Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

문제 42a

22장, 문제 42a

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?

검증된 단계별 안내

Step 1: Start by identifying the relevant formula for the electric force between two charges. The formula is Coulomb's Law:

F = k * (q_1 * q_2) / r^2

, where F is the electric force, k is Coulomb's constant (

8.99 × 10^9 \, N \, m^2 / C^2

q_1

and

q_2

are the charges, and r is the distance between the charges.

Step 2: Assign the given values to the variables. The force

F

is 0.45 N, the distance

r

is 10 cm (convert to meters:

r = 0.1 \, m

), and the relationship between the charges is

q_A = 2q_B

Step 3: Substitute

q_A = 2q_B

into Coulomb's Law. The equation becomes:

F = k * (2q_B * q_B) / r^2

, which simplifies to

F = k * (2q_B^2) / r^2

Step 4: Rearrange the equation to solve for

q_B

. The equation becomes:

q_B^2 = (F * r^2) / (2k)

. Take the square root to find

q_B

q_B = sqrt((F * r^2) / (2k))

Step 5: Once

q_B

is calculated, use the relationship

q_A = 2q_B

to find the charge on A. This completes the solution.

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주요 개념

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

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the electric force acting between charged objects, which is essential for solving the problem at hand.

Electric Charge

Electric charge is a 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 scenario, understanding the relationship between the charges of objects A and B is crucial for determining the charge on A based on the given force experienced by B.

Force Calculation

The calculation of force in physics often involves using formulas that relate mass, acceleration, and in this case, electric force. For charged objects, the force can be calculated using Coulomb's Law. Knowing the force experienced by B allows us to backtrack and find the charge on A, given that A has twice the charge of B.