A uniform charge distribution of total charge Q (Q>0) has endpoints located at (0.0m,12.0m) and (5.0m,0.0m). Assume the x-direction is horizontal and the y-direction is vertical. Our goal is to calculate the electric field at point P which is located at the origin.Draw a picture of the system and derive the equation of the line that represents the charge distribution. You are not allowed to rotate your coordinate system for this problem. (a) Determine the expression for dq. In this case the element of length of the charge distribution is written as ds=(dx^2+dy^2)1/2.You will need to write an equation for y in terms of x. (b) Determine the expression for r2, the magnitude of the vector that is directed from the element of charge dq to the location in which the field is to be determined. Eliminate the variable y by writing y in terms of x. (c) Determine the expression for r̂ the unit vector that is directed from the element of charge dq to the location in which the field is to be determined.Eliminate the variable y by writing y in terms of x. (d) Write the expression for d due to the element of charge dq. Express your result in terms of the variable x and numerical and physical constants. (e) Integrate the expression to determine the electric field at P. You may use online resources for this one. (f) Calculate the magnitude of the electric field
A uniform charge distribution of total charge Q (Q>0) has endpoints located at (0.0m,12.0m) and (5.0m,0.0m). Assume the x-direction is horizontal and the y-direction is vertical. Our goal is to calculate the electric field at point P which is located at the origin.Draw a picture of the system and derive the equation of the line that represents the charge distribution. You are not allowed to rotate your coordinate system for this problem.
(a) Determine the expression for dq. In this case the element of length of the charge distribution is written as ds=(dx^2+dy^2)1/2.You will need to write an equation for y in terms of x. (b) Determine the expression for r2, the magnitude of the vector that is directed from the element of charge dq to the location in which the field is to be determined. Eliminate the variable y by writing y in terms of x. (c) Determine the expression for r̂ the unit vector that is directed from the element of charge dq to the location in which the field is to be determined.Eliminate the variable y by writing y in terms of x. (d) Write the expression for d due to the element of charge dq. Express your result in terms of the variable x and numerical and physical constants. (e) Integrate the expression to determine the electric field at P. You may use online resources for this one. (f) Calculate the magnitude of the electric field.
Step by step
Solved in 5 steps with 5 images
