Suppose a point charge q has the trajectory ro(t) = at î, where a > 0. Suppose we want to calculate the scalar potential V for points on the negative z axis. (a) Calculate the separation vector i (t), the vector from the particle's location o to the field point on the negative z-axis. (b) Find 2 (t) = |ï (t)| %3D (c) Given your answer in part (b), use t, = t-2 (t,)/c to solve for t,. (The expression r (t,) means use t t, in your expression for r.) (d) Find the velocity of the particle, (t). (e) Evaluate the quantity 2 c-i i at time t t, where t, is given by the expression you found in part (c). (f) Use Equation 10.46 in the textbook and the quantity you calculated in part (e) to find V for points on the negative z axis. 1 qc v)' V (r,t) = 4TEo (c - : V) (10.46)

Suppose a point charge q has the trajectory ro(t) = at î, where a > 0. Suppose we want to calculate the scalar potential V for points on the negative z axis. (a) Calculate the separation vector i (t), the vector from the particle's location o to the field point on the negative z-axis. (b) Find 2 (t) = |ï (t)| %3D (c) Given your answer in part (b), use t, = t-2 (t,)/c to solve for t,. (The expression r (t,) means use t t, in your expression for r.) (d) Find the velocity of the particle, (t). (e) Evaluate the quantity 2 c-i i at time t t, where t, is given by the expression you found in part (c). (f) Use Equation 10.46 in the textbook and the quantity you calculated in part (e) to find V for points on the negative z axis. 1 qc v)' V (r,t) = 4TEo (c - : V) (10.46)

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 16OQ: A filament running along the x axis from the origin to x = 80.0 cm carries electric charge with...

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