Question

Notify Me Bookmark

21.79 CALC 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 (Fig. P21.79). (a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a. (b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q. (c) Show that if r≫a, the magnitude of the force in part (b) is approximately Qq/4πϵ0 r2. Explain why this result is obtained. Figure P21.79

21.79 CALC 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 (Fig. P21.79). (a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a. (b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q. (c) Show that if r≫a, the magnitude of the force in part (b) is approximately Qq/4πϵ0 r2. Explain why this result is obtained. Figure P21.79

Image text
21.79 CALC 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 (Fig. P21.79). (a) Calculate the x - and y -components of the electric field produced by the charge distribution Q at points on the positive x -axis where x > a . (b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q . (c) Show that if r ≫ a , the magnitude of the force in part (b) is approximately Q q / 4 π ϵ 0 r 2 . Explain why this result is obtained.
Figure P21.79

Detailed Answer

2 0

Please enter your email here. You will get email when this question is answered by our tutor.

Answer
Doubtrix Logo

This Problem has been solved!

You'll get a detailed, step-by-step and expert verified solution.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Login Sign Up
  • Student Reviews:
  • (2)
  • Correct answers (2)
  • Complete solution (2)
  • Step-by-step solution (2)
  • Fully explained (2)

Similar/Related Questions

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) Figure 1 of 1 Part A Calculate the x-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 some or all of the variables Q, a, x, and constant k. 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 some or all of the variables Q, a, y, r, and constant k. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms some or all of the variables Q, q, a, r, and constant k. Part D In what direction the charge distribution Q exerts force on q. to the left to the right

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) Figure 1 of 1 Part A Calculate the x-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 some or all of the variables Q, a, x, and constant k. 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 some or all of the variables Q, a, y, r, and constant k. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms some or all of the variables Q, q, a, r, and constant k. Part D In what direction the charge distribution Q exerts force on q. to the left to the right

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) Figure 1 of 1 Part A Calculate the x-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 some or all of the variables Q, a, x, and constant k. 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 some or all of the variables Q, a, y, r, and constant k. Part C Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms some or all of the variables Q, q, a, r, and constant k. Part D In what direction the charge distribution Q exerts force on q. to the left to the right
Solution
2 0

In the figure below, each charged particle is located at one of the four vertices of a square with side length = a. In the figure, A = 3, B = 4, and C = 3, and q > 0. (i) (a) What is the expression for the magnitude of the electric field in the upper right corner of the square (at the location of q )? (Use the following as necessary: q, a, and ke⋅) E = Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric field at this location. (counterclockwise from the +x-axis) (b) Determine the expression for the total electric force exerted on the charge q. (Enter the magnitude. Use the following as necessary: q, a, and ke. ) F = Give the direction angle (in degrees counterclockwise from the +x-axis) of the electric force on q. ∘ (counterclockwise from the +x-axis) (c) What If? How would the answers to parts (a) and (b) change if each of the four charges were negative with the same magnitude? Select all that apply. The force would be the same magnitude but opposite direction as the force in part (b). The electric field would be the same magnitude and direction as the field in part (a). The force would be the same magnitude and direction as the force in part (b). The electric field would be the same magnitude but opposite direction as the field in part (a).
Solution
0 0

Question 2 Apply what you know about conservation laws to the following questions. (a) Two protons are held fixed on the y-axis at y = a and y = −a. You release an electron (mass me) on the x-axis at x = 2 a. What is the maximum speed the electron will reach? (b) An electron (mass me) and proton (mass mp) are held a distance r apart. They are released simultaneously and begin to accelerate towards each other. What is the electron's speed by the time the distance between the charges has halved? Answers: (a) vmax = [e2 ameπϵ0(1−15)]1 /2 (b) ve = [14πϵ02 e2 mpme(me+mp)r]1 /2 Question 3 (a) Show that the electric field inside a solid charged sphere with a uniform charge density of ρ is E→(r→) = ρr→/(3ϵ0). Here r→ is a position vector relative to the centre of the sphere. Use known results for spherically symmetric charge distributions. (b) Suppose a spherical cavity is hollowed out of the sphere. The centre of the cavity is at position a→ relative to the centre of the sphere. Derive an expression for the electric field inside the cavity. You should find that it is perfectly uniform. Hint: Use your result in (a) together with the superposition principle.
Solution
0 0