An electric potential produced by some distribution of charge in a region is given by theequation V= 4xy2 - 3z²x + 15y²z with V in volts and the coordinates in meters. Determinethe z-component of electric field (in kV/m) at the point (1.0, 3.0, 2.0) m.

An object is said to be charged if it has an excess of either the negative or the positive charges.…

An electric potential produced by some distribution of charge in a region is given by the equation V=4xy² - 3z²x + 15y²z with V in volts and the coordinates in meters. Determine the z-component of electric field (in kV/m) at the point (1.0, 3.0, 2.0) m.

An electric potential produced by some distribution of charge in a region is given by the equation V=4xy² - 3z²x + 15y²z with V in volts and the coordinates in meters. Determine the z-component of electric field (in kV/m) at the point (1.0, 3.0, 2.0) m.

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 22P

See similar textbooks

Similar questions

The electric field in a region is radially outward with mag- nitude E = ar. Calculate the charge contained in a sphere of radius R centered at the origin. Calculate the value of charge if a = 100 V/m² and R = 0.30 m. R J Fig. 2.60 dr
Given is potential V(x,y,z) = 2x2+5y2+6z2-3xyz. where V is in volts and x, y, z are in %3D meters. Find the magnitude of the electric field at point (3,0,2). ( all coordinates in meters) State your answer to the nearest hundredth of the unit. (V/m).
The electric field is defined by the equation below in rectangular coordinates. Find VA if VB is 3 volts and points A and B are located at (-1, 3, 4) m and (0, -2, 5) m respectively, in free space.
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/ao + B/r + bo %| where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Va Edr= Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-"b/ao - era/ao) + B In( ) + bo ( ))
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/ao + B/r + bo %3D where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Vab = | S"Edr= - [ *Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-rb/ao - eralao) + B In( ) + bo ( ))
The electric field of a charge distribution is found to be E = f Eoe +). where Eo, µ are constant parameters and r is the radial distance to the origin of the coordinate system, which also coincides with the radial coordinate. r is the unit vector along the direction of increasing r. What is the corresponding electric potential at coordinate r, if the potential goes to zero as r o? Select one: V(r) = Eo, e ur V(r) = Eo e kr V (r) = E o V(r) = Eo
Answer All.Compute for the work done, in millijoules, in moving a 9-nC charge radially away from the center from a distance of 3 m to a distance of 7 m against the electric field inside a solid insulating sphere of radius 11 m and total charge 7 mC.Ans: -8.5199Determine the total potential energy, in microjoules, stored in a parallelepiped of dimensions are 9 m by 6 m by 8 m if the electric field inside is given as E = 17 ar + 19 aθ + 15 aϕ V/m. Use the permittivity of free space as 8.854 × 10-12 F/m.Ans: 1.6734If the electric field in the region is given as E = -cos(θ) sin( 4 Φ) aθ + b cos( 4 Φ) aφ V/m. Determine the potential at point A(4 m, 0.46 rad, 2.07 m), in volts, if the potential at point B(4 m, 1.00 rad, 0.10 m) is 60 volts. The value of b is also the coefficient of Φ.58.4552 Compute for the potential difference, in volts, in moving a charge from A(3, 2, -2) m to B(7, -6, 6) m against the electric field due to a disk charge of radius 9 m on the plane x = 0. The disk has a…
QUESTION 3 Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/ 24,2) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R…
Fill in the blanks.
A spherical conductor has a radius of 8 mm and a charge of 20μC. Calculate the electric field and the electric potential at:(a) r = 8 mm from the center (b) r = 12 mm and (c) r = 6 mm
Please fill in the blanks.
Charge E (10 microC), Charge F (2 microC), and Charge G (10 microC) are located in the cartesian plane with the following coordinates, respectively (0 cm, 5 cm), (0 cm, 0 cm), and (5 cm, 0 cm). Calculate the electric field at midpoint between Charge E and Charge F.