Homework Answers
The Electric field intensity can be found by using Gauss's Law(Maxwell's First equation) which is given as follows:
∯D.dS = ∫∫∫ρvdV
D= Electric Flux density
ρv=Volume charge density
Here surface S is the suitable Gaussian surface and in case of spherical coordinates most suitable Gaussian surface is a sphere.
Solution is given in the image attached.
Note: E= Electric field intensity
ε∘= Permittivity of free space
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nc = 13
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coordinate system) at observation point P(1, 1, -1). No need to
derive any expressions! Show main steps with proper units.
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nc = 13
1. Find the charge in the volume defined by 1<r<2m, in the spherical coordinates if pv = (No cos?0)/r* (uC/mº). 2. Given that D = 7r2 a, + Nc sin 0 ag in spherical coordinates, find the charge density. 3. Find the work done in moving a point charge Q = - 20 uC from (4,2,0)m to the origin in the field E = (x/2 + 2y) ax + Nc xay (V/m). 1
Q1.(25pts) A nonuniform volume charge distribution with density p,= 100 C/m3 , lies within the spherical region of radius a 0.2m in free space. a) Find the electric field intensity at a point outside the charge region. (9pts) b) Find the potential at the surface of the spherical charge region. (9pts) c) Determine the force acting on a charge of 10 Coulombs located at Px(5m, 90°, 90°), Indicate the position and orientation of the force vector on the sketch below....
1. In Free space, the planex 10 [m) carries a surface charge with the density p, - 20, ICIm']. The electric field intensity vector E [v/m] at the origin is: b). 10a, @n e) 10 ai d)-10 a.
An
infinitely long uniform line charge of 20 nC/m lie along the z axis
in free space, determine the electric flux density (in Cartesian
coordinate system) at observation point P(1, 1, -1). No need to
derive any expressions! Show main steps with proper units.
An infinitely long uniform line charge of 20 nC/m lie along the z axis in free space, determine the electric flux density (in Cartesian coordinate system) at observation point P(1, 1,-1). No need to derive any...
A hollow sphere has a uniform volume charge density of 1.78
nC/m3. The inner radius is a = 10.3 cm and the outer radius is b =
41.2 cm.
+4 +t1 +b+t A hollow sphere has a uniform volume charge density of 1.78 nC/m. The inner radius is a= 10.3 cm and the outer radius is b= 41.2 cm What is the magnitude of the electric field at 16.5 cm from the center of the sphere? What is the magnitude...
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ: 0 if r R where γ is a constant a) What units must the constant γ have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r R. (Hint: if the charge distribution is spherically symmetric, what can you say...
31. In free space, infinite planes y-4 m and y -8m carry charges of 20 nC/m2 and 30 nC/m2, respectively. If plane y-2 m is grounded, calculate the electric field intensity at (-4 m, 6 m, 2 m).
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