Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

문제 65c

22장, 문제 65c

A 10.0 nC charge is located at position (x, y)=(1.0 cm, 2.0 cm). At what (x, y) position(s) is the electric field $open paren 21 comma 600 i hat minus 28 comma 800 j hat close paren$ N/C?

검증된 단계별 안내

Step 1: Recall the formula for the electric field due to a point charge:

E = k_e * |q| / r^2

, where

k_e

is Coulomb's constant (

8.99 × 10^9 \, N \, m^2 / C^2

q

is the charge, and

r

is the distance from the charge to the point where the field is being calculated.

Step 2: The electric field is a vector quantity, so it has both magnitude and direction. The given electric field vector is

E = (21,600 \, \(\hat{i}\) - 28,800 \, \(\hat{j}\)) \, N/C

. This means the field has components in the x-direction and y-direction. Use the relationship

E_x = k_e * |q| * (x - x_0) / r^3

and

E_y = k_e * |q| * (y - y_0) / r^3

, where

(x_0, y_0)

is the position of the charge.

Step 3: Calculate the distance

r

from the charge to the point where the electric field is given. Use the formula

r = \(\sqrt{(x - x_0)^2 + (y - y_0)^2}\)

. Substitute

(x_0, y_0) = (1.0 \, \(\text{cm}\), 2.0 \, \(\text{cm}\))

and solve for

r

Step 4: Solve for the coordinates

(x, y)

by equating the given electric field components to the expressions for

E_x

and

E_y

. This will involve solving the system of equations:

21,600 = k_e * |q| * (x - x_0) / r^3

and

-28,800 = k_e * |q| * (y - y_0) / r^3

Step 5: Rearrange the equations to isolate

x

and

y

. Substitute the known values of

k_e

q = 10.0 \, \(\text{nC}\) = 10.0 × 10^{-9} \, C

, and

(x_0, y_0)

. Solve the system of equations to find the coordinates

(x, y)

where the electric field has the given components.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

15m

주요 개념

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

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 experienced by a positive test charge placed in the field. The direction of the electric field is away from positive charges and towards negative charges, and its magnitude is measured in newtons per coulomb (N/C).

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two point charges 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 field generated by a point charge, as it helps determine the force experienced by other charges in the field.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a resultant vector. In the context of electric fields, each charge contributes to the total electric field at a point, and these contributions must be added as vectors, taking into account their magnitudes and directions. This is crucial for solving problems involving multiple charges and determining the net electric field at a specific location.