Explanation Given data: The current density J is R ^ 5 R A / m 2 . The radius R of the given sphere is 5 m . Calculation: Write the standard expression for the current for given current density is, I = ∫ s J ⋅ d s (1) Here, I is the current. d s is the differential surface. Write the standard expression for differential surface in Cartesian coordinates. d s = R ^ R 2 sin θ d θ d ϕ + θ ^ R sin θ d R d ϕ + ϕ ^ R d R d θ Here, R ^ is the unit vector along the radius vector. θ ^ is the unit vector along the polar angle coordinate vector. ϕ ^ is the unit vector along the azimuthal angle coordinate vector. Substitute R ^ 5 R A / m 2 for J , 0 for θ 1 , π for θ 2 , 0 for ϕ 1 , 2 π for ϕ 2 , and R ^ R 2 sin θ d θ d ϕ + θ ^ R sin θ d R d ϕ + ϕ ^ R d R d θ for d s in equation (1). I = ∫ θ 1 = 0 θ 2 = 2 ∫ ϕ 1 = 0 ϕ 2 = 2 ( R ^ 5 R A / m 2 ) ⋅ ( R ^ R 2 sin

7th Edition

ISBN: 8220100663659

Author: ULABY

Publisher: PEARSON

See similar textbooks

Concept explainers

Solenoidal Vector Field

In Physics and Mathematics vector calculus attached to each point in a subset of space, there is an assignment of a vector in a field called a vector field.

Question

Chapter 4, Problem 7P

To determine

The current flowing through the given surface.

Expert Solution & Answer

Chapter 4 Solutions

EBK FUNDAMENTALS OF APPLIED ELECTROMAGN

Ch. 4.2 - What happens to Maxwells equations under static...Ch. 4.2 - How is the current density J related to the volume...Ch. 4.2 - Prob. 3CQ Ch. 4.2 - A square plate residing in the xy plane is...Ch. 4.2 - A thick spherical shell centered at the origin...Ch. 4.3 - When characterizing the electrical permittivity of...Ch. 4.3 - If the electric field is zero at a given point in...Ch. 4.3 - State the principle of linear superposition as it...Ch. 4.3 - Four charges of 10 C each are located in free...Ch. 4.3 - Two identical charges are located on the x axis at...

Ch. 4.3 - In a hydrogen atom the electron and proton are...Ch. 4.3 - An infinite sheet with uniform surface charge...Ch. 4.4 - Explain Gausss law. Under what circumstances is it...Ch. 4.4 - How should one choose a Gaussian surface?Ch. 4.4 - Two infinite lines, each carrying a uniform charge...Ch. 4.4 - A thin spherical shell of radius a carries a...Ch. 4.4 - A spherical volume of radius a contains a uniform...Ch. 4.5 - What is a conservative field?Ch. 4.5 - Why is the electric potential at a point in space...Ch. 4.5 - Prob. 11CQ Ch. 4.5 - Why is it usually easier to compute V for a given...Ch. 4.5 - Prob. 13CQ Ch. 4.5 - Determine the electric potential at the origin due...Ch. 4.5 - A spherical shell of radius a has a uniform...Ch. 4.6 - What are the electromagnetic constitutive...Ch. 4.6 - Prob. 15CQ Ch. 4.6 - What is the conductivity of a perfect dielectric?Ch. 4.6 - Prob. 17CQ Ch. 4.6 - Prob. 18CQ Ch. 4.6 - Determine the density of free electrons in...Ch. 4.6 - Prob. 13E Ch. 4.6 - A 50 m long copper wire has a circular cross...Ch. 4.6 - Prob. 15E Ch. 4.7 - What is a polar material? A nonpolar material?Ch. 4.7 - Prob. 20CQ Ch. 4.7 - What happens when dielectric breakdown occurs?Ch. 4.7 - Find E1 in Fig. 4-19 if E2=x2y3+z3(v/m),1=20,2=80,...Ch. 4.7 - Repeat Exercise 4.16 for a boundary with surface...Ch. 4.8 - What are the boundary conditions for the electric...Ch. 4.8 - Prob. 23CQ Ch. 4.9 - How is the capacitance of a two-conductor...Ch. 4.9 - What are fringing fields and when may they be...Ch. 4.10 - To bring a charge q from infinity to a given point...Ch. 4.10 - Prob. 27CQ Ch. 4.10 - The radii of the inner and outer conductors of a...Ch. 4.11 - What is the fundamental premise of the image...Ch. 4.11 - Given a charge distribution, what are the various...Ch. 4.11 - Use the result of Example 4-13 to find the surface...Ch. 4 - A cube 2 m on a side is located in the first...Ch. 4 - Prob. 2P Ch. 4 - Find the total charge contained in a round-top...Ch. 4 - If the line charge density is given by l = 24y2...Ch. 4 - Find the total charge on a circular disk defined...Ch. 4 - If J = 4xz (A/m2), find the current I flowing...Ch. 4 - Prob. 7P Ch. 4 - An electron beam shaped like a circular cylinder...Ch. 4 - Prob. 9P Ch. 4 - A line of charge of uniform density occupies a...Ch. 4 - A square with sides of 2 m has a charge of 40 C at...Ch. 4 - Three point charges, each with q = 3 nC, are...Ch. 4 - Charge q1 = 6 C is located at (1 cm, 1 cm, 0) and...Ch. 4 - A line of charge with uniform density = 8 (C/m)...Ch. 4 - Prob. 15P Ch. 4 - A line of charge with uniform density l extends...Ch. 4 - Repeat Example 4-5 for liie circular disk of...Ch. 4 - Multiple charges at different locations are said...Ch. 4 - Three infinite lines of charge, all parallel to...Ch. 4 - Prob. 20P Ch. 4 - A horizontal strip lying in the xy plane is of...Ch. 4 - Prob. 22P Ch. 4 - Prob. 23P Ch. 4 - Charge Q1 is uniformly distributed over a thin...Ch. 4 - The electric flux density inside a dielectric...Ch. 4 - Prob. 26P Ch. 4 - An infinitely long cylindrical shell extending...Ch. 4 - If the charge density increases linearly with...Ch. 4 - A spherical shell with outer radius b surrounds a...Ch. 4 - Prob. 30P Ch. 4 - Prob. 31P Ch. 4 - A circular ring of charge of radius a lies in the...Ch. 4 - Prob. 33P Ch. 4 - Find the electric potential V at a location a...Ch. 4 - For the electric dipole shown in Fig. 4-13, d = 1...Ch. 4 - For each of the distributions of the electric...Ch. 4 - Two infinite lines of charge, both parallel to the...Ch. 4 - Given the electric field E=R18R2(V/m) find the...Ch. 4 - An infinitely long line of charge with uniform...Ch. 4 - The xy plane contains a uniform sheet of charge...Ch. 4 - A cylindrical bar of silicon has a radius of 4 mm...Ch. 4 - Repeat Problem 4.41 for a bar of germanium with e...Ch. 4 - A 100 m long conductor of uniform cross-section...Ch. 4 - Prob. 44P Ch. 4 - Apply the result of Problem 4.44 to find the...Ch. 4 - A 2 103 mm thick square sheet of aluminum has 5 cm...Ch. 4 - A cylinder-shaped carbon resistor is 8 cm in...Ch. 4 - With reference to Fig. 4-19, find E1 if...Ch. 4 - An infinitely long cylinder of radius a is...Ch. 4 - If E=R150(V/m) at the surface of a 5-cm conducting...Ch. 4 - Figure P4.51 shows three planar dielectric slabs...Ch. 4 - Determine the force of attraction in a...Ch. 4 - Dielectric breakdown occurs in a material whenever...Ch. 4 - An electron with charge Qe = 1.61019 C and mass me...Ch. 4 - In a dielectric medium with r = 4, the electric...Ch. 4 - Prob. 56P Ch. 4 - Prob. 57P Ch. 4 - Prob. 58P Ch. 4 - Prob. 59P Ch. 4 - Prob. 60P Ch. 4 - Prob. 61P Ch. 4 - Conducting wires above a conducting plane carry...Ch. 4 - Prob. 63P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

The current flowing through the given surface.

Solution Summary: The author calculates the standard expression for the current flowing through the given surface.

Concept explainers

The current flowing through the given surface.

Chapter 4 Solutions