A −4.00-4.00-nC point charge is at the origin, and a second −5.00-5.00-nC point charge is on the xx-axis at x=0.800x = 0.800 m. Find the electric field (magnitude and direction) at each of the following points on the xx-axis: (i) x=0.200x = 0.200 m; (ii) x=1.20x = 1.20 m; (iii) x=−0.200x = -0.200 m.

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

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Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

문제 40a

21장, 문제 40a

A $negative 4.00$ -nC point charge is at the origin, and a second $negative 5.00$ -nC point charge is on the $x$ -axis at $x equals 0.800$ m. Find the electric field (magnitude and direction) at each of the following points on the $x$ -axis: (i) $x equals 0.200$ m; (ii) $x equals 1.20$ m; (iii) $x = - 0.200$ m.

검증된 단계별 안내

Step 1: Understand the concept of electric field due to a point charge. The electric field $ E $ created by a point charge $ q $ at a distance $ r $ is given by $ E = \frac{k \cdot |q|}{r^2} $, where $ k $ is Coulomb's constant $ 8.99 \times 10^9 \text{ N m}^2/\text{C}^2 $. The direction of the electric field is away from the charge if it is positive and towards the charge if it is negative.

Step 2: Calculate the electric field at each specified point on the x-axis due to each charge separately. For point (i) at $ x = 0.200 \text{ m} $, calculate the electric field due to the charge at the origin and the charge at $ x = 0.800 \text{ m} $. Use the formula $ E = \frac{k \cdot |q|}{r^2} $ for each charge, considering the distance from the charge to the point.

Step 3: Determine the direction of the electric field at each point. Since both charges are negative, the electric field at any point will be directed towards each charge. Sum the electric fields vectorially, taking into account their directions, to find the net electric field at each point.

Step 4: Calculate the net electric force on an electron at each point using the formula $ F = q_e \cdot E_{net} $, where $ q_e $ is the charge of an electron $ -1.60 \times 10^{-19} \text{ C} $. Use the net electric field calculated in the previous step for each point.

Step 5: Consider the direction of the force on the electron. Since the electron has a negative charge, the force direction will be opposite to the direction of the net electric field at each point. Analyze the results to understand how the electron would move in response to the forces at each location.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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주요 개념

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

Electric Field

The electric field is a vector field around a charged object where a force would be exerted on other charges. It is defined as the force per unit charge and is measured in newtons per coulomb (N/C). The direction of the electric field is the direction of the force it would exert on a positive test charge.

Superposition Principle

The superposition principle states that the net electric field created by multiple charges is the vector sum of the individual fields produced by each charge. This principle allows us to calculate the total electric field at a point by adding the fields due to each charge, considering both magnitude and direction.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The force is attractive if the charges are opposite and repulsive if they are the same.