   Chapter 15.4, Problem 1E

Chapter
Section
Textbook Problem

Electric charge is distributed over the rectangle 0 ≤ x ≤ 5, 2 ≤ y ≤ 5 so that the charge density at (x, y) is σ(x, y) = 2x + 4y (measured in coulombs per square meter). Find the total charge on the rectangle.

To determine

To find: The total charge over the given rectangular region.

Explanation

Given:

The rectangle R is 0x5,2y5.

The charge density at (x,y) is σ(x,y)=2x+4y.

Formula used:

The total charge Q on the given rectangular region R is, Q=Rσ(x,y)dA.

Here, the charge density is given by σ(x,y).

Calculation:

Total charge Q on the given rectangle R is,

Q=Rσ(x,y)dA=0525(2x+4y)dydx

Integrate with respect to y,

Q=05[2xy+4y22]25dx=05[2xy+2y2]25dx=205[xy+y2]25dx

Apply the limit value of y,

Q=2

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find f in terms of g. f(x) = g(g(x))

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 1-6, solve for y. (x2)2+(y+1)2=9

Calculus: An Applied Approach (MindTap Course List)

Expand each expression in Exercises 122. (2x2)(3x4)

Finite Mathematics and Applied Calculus (MindTap Course List)

Identify the type of fraction and write it in word form. 2.

Contemporary Mathematics for Business & Consumers

Construct a 135 angle.

Elementary Geometry For College Students, 7e

0 1 ∞

Study Guide for Stewart's Multivariable Calculus, 8th 