Homework Answers
To solve above question we will use continuity equation in
electromagnetism.Please see in the attached image.
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Continuity equation for electric charge. Suppose there is a volume current density given by 7-(i)-(sinx,cosx,) a....
9. Suppose we have some charge density ρ(t,x) in space and a current density J(t, x),...
9. Suppose we have some charge density ρ(t,x) in space and a current density J(t, x), and suppose both quantities are known to be zero outside of a sphere of some radius R. Use the conservation equation to show that the total charge Q(t) dxdydz ρ(t, x) Jall of space is (a) finite and (b) conserved, ie, IQI 〈 x and Q-0.*
A uniform volume charge occupies the region r < a and has volume charge density ρ....
A uniform volume charge occupies the region r < a and has volume charge density ρ. The total charge of the volume charge is +2Q. A thin spherical shell of radius b > a surrounds the volume charge. The total charge of the thin spherical shell is −2Q. (a)Draw the electric field map with 4 lines per Q on the figure to the right. (b)Calculate the electric field everywhere. This part is to be worked symbolically (no decimal numbers should...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Please help. 1. The volume current density in a medium is given as I = eBP...
Please help.
1. The volume current density in a medium is given as I = eBP cospê - In (cosBz)2 A/m². Determine the time rate of change of the volume charge density. (3 points)
#1 and #3 I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer...
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney,...
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)
The electric potential of a charge distribution is given by the equation VKY.Z) = 2xy-372 -42where...
The electric potential of a charge distribution is given by the equation VKY.Z) = 2xy-372 -42where x,y,z are measured in meters and Vis measured in volts. Calculate the magnitude of the electric field vector at the position xyz)-(1.0, 1.0, 1.0). Select one: O a. 14.2 V/m b. 18.2 V/m O C. 12.2 V/m d. 10.2 Vim ОО e. 16.2 Vim
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
a) Derive from the definition of the clectric current I = [s df - j through...
a) Derive from the definition of the clectric current I = [s df - j through the arca S the dwhere dQ is the charge formula for the electric current inside a conducting wire I which flows through the cross section of the wire in the time dt stationary charge distribution, 2n wire have to be equal and independent of the cross sections of the wire both ends of the b) Show that for a 0, the currents on OSS...
given a solid wire of radius R in which there is a volume current density J=...
given a solid wire of radius R in which there is a volume current density J= a/s solve for a, do not leave a in solution. Calculate total current I (s is radial term) Find magnetic field inside find magnetic vector potential A inside
9. Suppose we have some charge density ρ(t,x) in space and a current density J(t, x), and suppose both quantities are known to be zero outside of a sphere of some radius R. Use the conservation equation to show that the total charge Q(t) dxdydz ρ(t, x) Jall of space is (a) finite and (b) conserved, ie, IQI 〈 x and Q-0.*
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Please help.
1. The volume current density in a medium is given as I = eBP cospê - In (cosBz)2 A/m². Determine the time rate of change of the volume charge density. (3 points)
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)
The electric potential of a charge distribution is given by the equation VKY.Z) = 2xy-372 -42where x,y,z are measured in meters and Vis measured in volts. Calculate the magnitude of the electric field vector at the position xyz)-(1.0, 1.0, 1.0). Select one: O a. 14.2 V/m b. 18.2 V/m O C. 12.2 V/m d. 10.2 Vim ОО e. 16.2 Vim
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
a) Derive from the definition of the clectric current I = [s df - j through the arca S the dwhere dQ is the charge formula for the electric current inside a conducting wire I which flows through the cross section of the wire in the time dt stationary charge distribution, 2n wire have to be equal and independent of the cross sections of the wire both ends of the b) Show that for a 0, the currents on OSS...
given a solid wire of radius R in which there is a volume current density J= a/s solve for a, do not leave a in solution. Calculate total current I (s is radial term) Find magnetic field inside find magnetic vector potential A inside
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