Would be able to help me answer this please? Consider a straight, non-conducting rod of length L that is charged such that its charge density increases linearly from zero at one end to a maximum λₒ at the other. Derive an expression for the total charge on the conductor in terms of L and λₒ. I know that the total charge density is equal to αx (α being a constant and x being a small amount of L), and that dq=λdx and that you integrate, but how am I meant to get it in terms of λₒ and L ???

Would be able to help me answer this please? Consider a straight, non-conducting rod of length L that is charged such that its charge density increases linearly from zero at one end to a maximum λₒ at the other. Derive an expression for the total charge on the conductor in terms of L and λₒ. I know that the total charge density is equal to αx (α being a constant and x being a small amount of L), and that dq=λdx and that you integrate, but how am I meant to get it in terms of λₒ and L ???

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 15P: Use the orders of magnitude you found in the previous problem to answer the following questions to...

See similar textbooks

Similar questions

part 1 of 2 Consider the field due to a uniformly charged disk of radius R and charge Q. Along the symmetry axis at distance z from the cen- ter, the field has been written in following forms. where Eexact = Eo (1 。 (1-√R²+²) (1-7) E₁ ≈ Eo (1 R part 2 of 2 Eo = (Q/A) 280 To compare the accuracy of different ap- proximations it is convenient to work with the normalized difference to be specified below. The nth order smallness is charac- terized by e" and € = 3 with e being the smallness parameter. In general the nth or- der term takes the form Ce", where C is some finite constant (e.g 0.1
part 1 of 2 Consider the field due to a uniformly charged disk of radius R. and charge Q. Along the symmetry axis at distance z from the cen- ter, the field has been written in following forms. where Eexact = Eo E₁ Eo part 2 of 2 2 R² + z² (1-7) (Q/A) 280 Eo = To compare the accuracy of different ap- proximations it is convenient to work with the normalized difference to be specified below. The nth order smallness is charac- terized by e" and € = with being the R smallness parameter. In general the nth or- der term takes the form Ce", where C is some finite constant (e.g 0.1 < C < 10). Eexact - E1| For the normalized difference Eo identify the correct choice among the follow- ing |E1 - Eo For the normalized difference Eo identify the correct choice among the follow- ing 1. 2. €³ 3. €2 4. € 1. € 2. €³ 3. €² 4. €4
What Uniform Electric Field Strength must be developed across parallel conductive plates that are separated by 1 meter in order for a body of mass 1 microgram and charge +1 nC to transit the plate gap in 1 ms? See illustration below. 1m E=? H + T=1 ms 1 μg 1 nC Choose the best answer from the list below. Show your work per the problem solving rubric and submit in the following question. A. 1X105 N/C B. 2X106 N/C C. 3X10 N/C D. 4X108 N/C Guiding Questions: ▪ Determine the acceleration, a, needed to transit in time t. ▪ Determine the force, f, needed to generate acceleration a. ▪ Determine the Electric Field necessary to generate force f.
A sphere of radius R has total charge Q. The volume charge density (C/m') within the sphere is p(r) = C/r² , where C is a constant to be determined. 1. Use the expression to find a magnitude of an electric field strenght E : a) inside the sphere (r
Fig.2
Consider a rod of length L carrying a charge of q distributed uniformly over its length. Where applicable, let V(r → ∞) = 0. Hint q a. What is the voltage V at point P (at distance a away from the near end of the rod) due to the charge over the length of the rod? Express your answer in terms of given parameters (L,q,a) and physical constants (ke, Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for (a) E = Vp = b. Calculate the electric field at point P by differentiating V with respect to a. Let positive sign of E indicate direction of electric field pointing away from the rod. Hint for (b) a Question Help: Message instructor Submit Question с MacBook Pro G Search or type URL ☆ +
The figure (Fig. 1) shows a long cylindrical capacitor consists of a solid conducting core with radius r1=9mm and outer hollow conducting tube with an inner radius of r2=35mm. The length of the capacitor is L=28cm. Figure 2 is the cross sectional view of the system. This system of rod and shell is connected to a voltage source of emf E=6.8volts. There is no dielectric material present in the system as of now. a) Calculate the capacitance of the capacitor b) Say the inner rod is negatively charged. Given this, calculate the charge density of the outer surface. And show how the electric field lines are oriented in this system. Hint: you can use the cross section for this (Fig. 2).
The figure (Fig. 1) shows a long cylindrical capacitor consists of a solid conducting core with radius r1=7mm and outer hollow conducting tube with an inner radius of r2=29mm . The length of the capacitor is L=32cm . Figure 2 is the cross sectional view of the system. This system of rod and shell is connected to a voltage source of emf E=6.4volts . There is no dielectric material present in the system as of now.
Imagine that two parallel plates are charged to achieve a voltage difference Vo between the plates. They have area A and spacing d. The plates are then electrically isolated so that no charge can be added or taken away. A good conductor of thickness d/2 is placed in between the two plates, as shown. How great is the charge density on the surface of the conductor relative to that on either of the plates? Why? (You may use infinite plane approximations for the surfaces.)
In Fig. 1, two parallel-plate capacitors (with air between theplates) are connected to a battery. Capacitor 1 has a plate areaof 1.5 cm2and an electric field (between its plates) ofmagnitude 2000 V/m. Capacitor 2 has a plate area of 0.70 cm2and an electric field of magnitude 1500 V/m. What is the totalcharge on the two capacitors?
Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. (Figure 1) Part A Calculate the x-component of the electric field produced by the charge distribution Qat points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part B Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, r, and appropriate constants. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q.Part D In what direction the charge distribution Q exerts force on q. In what direction the charge distribution exerts force on .to the left to the right
Consider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to λ this line of charge is given by E= 2kef= -, where is a unit vector directed radially outward Σπερμ from the infinitely long wire of charge. Hint #3 a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A,ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation 3 V(r) = b. There is a reason we are not setting V(r → ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(ro), with our current…