Electric potential function The electric potential in the xy-planeassociated with two positive charges, one at (0, 1) with twice themagnitude of the charge at (0, –1), is1p(x, y)V + (y – 1)²Vx? + (y + 1)²a. Compute o, and 4,-b. Describe how ç, and o, behave as x, y→ to.c. Evaluate o (0, y), for all y + + 1. Interpret this result.d. Evaluate o, (x, 0), for all a. Interpret this result.

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Q1. What is the electric potential of a dipole on the y-axis at large distances? 1 qd 1 qd (c) V = 2nɛ, r? 1 qd 4πε r (a) V = 0 (b) V = (d) V = 2πε, r y Q2. Find the monopole term in the multi-pole expansion of the electric potential on the z- axis for a flat circular charged disk of radius R and charge density o (r,q) = krʻ cosʻ q, where k is a constant and r, q are polar coordinates with the origin at the disk's centre.
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can u help with part c asap plz
Find the force vector F on an object of mass m the uniform gravitational field when it is at height z = 0. The +z direction is up. Express vector force in terms of m, z. g. and k, where k is the unit vector in the +z direction. To create the k character: In the equation editor window, select "More", then select "Vectors", and you will find what you need. To write out a vector: for example, if the answer has both x and y components, you would answer in the format Fi + Fj F(z) = -mgk Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector. Express U(z) in terms of m. z. and g. U(2)= In what direction does the object accelerate when released with initial velocity upward? downward Oupward or downward depending on the initial mass m. upward or downward depending on the initial velocity upward Now consider the analogous case of a particle…
Q-2: Two concentric conducting spherical shells of radii r¡ and r, > rz. The inner shell carries a charge +Q while the outer shell carries a charge +2Q as shown. Assuming V = 0 as r → ∞, Calculate: a. The electric field vectors: E1(r r2) b. The electric potentials: V, (r r2) c. The electric potential difference between the two shells: AV
The charge density on a disk of radius R = 11.6 cm is given by o = ar, with a = 1.46 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 44.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R A
Two large charged plates of charge density ±18µC/m² face each other at a separation of 7 mm. Choose coordinate axes so that both plates are parallel to the xy plane, with the negatively charged plate located at z = 0 and the positively charged plate at z = +7 mm. Define potential so that potential at z = 0 is zero (V(z = 0) = 0). Hint a. Find the electric potential at following values of z: o potential at z = -7 mm: V(z = -7 mm) = o potential at z = +1 mm: V(z = +1 mm): = o potential at z = +7 mm: V(z = +7 mm) = = o potential at z = +9.2 mm: V(z = +9.2 mm) = V. V. V. V. b. An electron is released from rest at the negative plate. With what speed will it strike the positive plate? The electron will strike the positive plate with speed of m/s. (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2, enter "3.14E12".)
d and e
The charge density on a disk of radius R = 11.2 cm is given by o = ar, with a = 1.30 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 30.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. R A A
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