University Physics (14th Edition)
University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 23, Problem 23.78P

CALC The electric potential V in a region of space is given by

V ( x ,   y ,   z )   =   A ( x 2     3 y 2 +   z 2 )

where A is a constant, (a) Derive an expression for the electric field E at any point in this region, (b) The work done by the field when a 1.50-μC test charge moves from the point (x, y, z) = (0, 0, 0.250 m) to the origin is measured to be 6.00 × 10−5J. Determine A. (c) Determine the electric field at the point (0, 0, 0.250 m). (d) Show that in every plane parallel to the xz-plane the equipotential contours arc circles, (e) What is the radius of the equipotential contour corresponding to V = 1280 V and y = 2.00 m?

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Chapter 23 Solutions

University Physics (14th Edition)

Ch. 23 - It is easy to produce a potential difference of...Ch. 23 - If the electric potential at a single point is...Ch. 23 - Because electric field lines and equipotential...Ch. 23 - A uniform electric field is directed due east....Ch. 23 - We often say that if point A is at a higher...Ch. 23 - A conducting sphere is to be charged by bringing...Ch. 23 - In electronics it is customary to define the...Ch. 23 - A conducting sphere is placed between two charged...Ch. 23 - A conductor that carries a net charge Q has a...Ch. 23 - A high-voltage dc power line falls on a car, so...Ch. 23 - When a thunderstorm is approaching, sailors at sea...Ch. 23 - A positive point charge is placed near a very...Ch. 23 - A point charge q1 = +2.40 C is held stationary at...Ch. 23 - A point charge q1 is held stationary at the...Ch. 23 - Energy of the Nucleus. How much work is needed to...Ch. 23 - (a) How much work would it take to push two...Ch. 23 - A small metal sphere, carrying a net charge of q1...Ch. 23 - BIO Energy of DNA Base Pairing. (See Exercise...Ch. 23 - Two protons, starting several meters apart, are...Ch. 23 - Three equal 1.20-C point charges are placed at the...Ch. 23 - Two protons are released from rest when they are...Ch. 23 - Four electrons are located at the corners of a...Ch. 23 - Three point charges, which initially are...Ch. 23 - An object with charge q = 6.00 109 C is placed in...Ch. 23 - A small particle has charge 5.00 C and mass 2.00 ...Ch. 23 - A particle with charge +4.20 nC is in a uniform...Ch. 23 - A charge of 28.0 nC is placed in a uniform...Ch. 23 - Two stationary point charges +3.00 nC and +2.00 nC...Ch. 23 - Point charges q1 = + 2.00 C and q2 = 2.00 C are...Ch. 23 - Two point charges of equal magnitude Q are held a...Ch. 23 - Two point charges q1 = +2.40 nC and q2 = 6.50 nC...Ch. 23 - (a) An electron is to be accelerated from 3.00 ...Ch. 23 - A positive charge q is fixed at the point x = 0, y...Ch. 23 - At a certain distance from a point charge, the...Ch. 23 - A uniform electric field has magnitude E and is...Ch. 23 - For each of the following arrangements of two...Ch. 23 - A thin spherical shell with radius R1 = 3.00 cm is...Ch. 23 - A total electric charge of 3.50 nC is distributed...Ch. 23 - A uniformly charged, thin ring has radius 15.0 cm...Ch. 23 - A solid conducting sphere has net positive charge...Ch. 23 - Charge Q = 5.00 C is distributed uniformly over...Ch. 23 - An infinitely long line of charge has linear...Ch. 23 - A very long wire carries a uniform linear charge...Ch. 23 - A very long insulating cylinder of charge of...Ch. 23 - A very long insulating cylindrical shell of radius...Ch. 23 - A ring of diameter 8.00 cm is fixed in place and...Ch. 23 - A very small sphere with positive charge q = +...Ch. 23 - CP Two large, parallel conducting plates carrying...Ch. 23 - Two large, parallel, metal plates carry opposite...Ch. 23 - BIO Electrical Sensitivity of Sharks. Certain...Ch. 23 - The electric field at the surface of a charged,...Ch. 23 - (a) How much excess charge must be placed on a...Ch. 23 - CALC A metal sphere with radius ra is supported on...Ch. 23 - A very large plastic sheet carries a uniform...Ch. 23 - CALC In a certain region of space, the electric...Ch. 23 - CALC In a certain region of space the electric...Ch. 23 - A metal sphere with radius ra = 1.20 cm is...Ch. 23 - CP A point charge q1, = +5.00 C is held fixed in...Ch. 23 - A point charge q1 = 4.00 nC is placed at the...Ch. 23 - A positive point charge q1 = +5.00 104 C is held...Ch. 23 - A gold nucleus has a radius of 7.3 1015 m and a...Ch. 23 - A small sphere with mass 5.00 107 kg and charge...Ch. 23 - Determining the Size of the Nucleus. When...Ch. 23 - CP A proton and an alpha particle are released...Ch. 23 - A particle with charge +7.60 nC is in a uniform...Ch. 23 - Identical charges q = +5.00 C are placed at...Ch. 23 - CALC A vacuum tube diode consists of concentric...Ch. 23 - Two oppositely charged, identical insulating...Ch. 23 - An Ionic Crystal. Figure P23.57 shows eight point...Ch. 23 - (a) Calculate the potential energy of a system of...Ch. 23 - CP A small sphere with mass 1.50 g hangs by a...Ch. 23 - Two spherical shells have a common center. The...Ch. 23 - CALC Coaxial Cylinders. A long metal cylinder with...Ch. 23 - A Geiger counter detects radiation such as alpha...Ch. 23 - CP Deflection in a CRT. Cathode-ray tubes (CRTs)...Ch. 23 - CP Deflecting Plates of an Oscilloscope. The...Ch. 23 - Electrostatic precipitators use electric forces to...Ch. 23 - CALC A disk with radius R has uniform surface...Ch. 23 - CALC Self-Energy of a Sphere of Charge. A solid...Ch. 23 - CALC A thin insulating rod is bent into a...Ch. 23 - Charge Q = +4.00 C is distributed uniformly over...Ch. 23 - An insulating spherical shell with inner radius...Ch. 23 - CP Two plastic spheres, each carrying charge...Ch. 23 - (a) If a spherical raindrop of radius 0.650 mm...Ch. 23 - CALC Electric charge is distributed uniformly...Ch. 23 - An alpha particle with kinetic energy 9.50 MeV...Ch. 23 - Two metal spheres of different sizes are charged...Ch. 23 - A metal sphere with radius R1 has a charge Q1....Ch. 23 - Prob. 23.77PCh. 23 - CALC The electric potential V in a region of space...Ch. 23 - DATA The electric potential in a region that is...Ch. 23 - DATA A small, stationary sphere carries a net...Ch. 23 - DATA The Millikan Oil-Drop Experiment. The charge...Ch. 23 - CALC A hollow, thin-walled insulating cylinder of...Ch. 23 - CP In experiments in which atomic nuclei collide,...Ch. 23 - For a particular experiment, helium ions are to be...Ch. 23 - A helium ion (He++) that comes within about 10 fm...Ch. 23 - The maximum voltage at the center of a typical...
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