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PROBLEM 3 (20 points) (A) Consider a line charge distribution, with uniform density A, along the...
Starting from Coulomb's law in integral form in terms of the charge density and a volume...
Starting from Coulomb's law in integral form in terms of the charge density and a volume integration, calculate the electric field at the origin of coordinates for a uniform line charge density λ that extends from (x,y,z) = (R,0,0) to (0,R,0) along an arc of radius R. 4.
A line of charge with uniform density of 32.0 nC/m lies along the line y =...
A line of charge with uniform density of 32.0 nC/m lies along the line y = -15.0 cm, between the points with coordinates x = 0 and x = 48.0 cm. Find the electric field it creates at the origin. Magnitude N/C Direction ° (counterclockwise from the +x axis)
2. A line of charge with uniform density of 38.0 nC/m lies along the line y...
2. A line of charge with uniform density of 38.0 nC/m lies along the line y 12.0 cm between the points x 5.0 cm and 40.0 cm. Calculate the electric field (both the magnitude and direction) at the origin due to this charge distribution. (2436 N/C, 137.9°)
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p....
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
Consider a charged ring with radius R and uniform line charge density +λ.
Consider a charged ring with radius R and uniform line charge density +λ.(a) Find the electric field at the center O of the ring. (b) What is the electric field at a field point P which is on the central axis with a distance z above the center? (c) Show that in the limit when z » R, the electric field reduces to the form Does this result physically make sense? Explain. (d) Using binomial approximation, , find the electric field at points along the...
A line of charge with uniform density of 38.0 nC/m lies along the line y =...
A line of charge with uniform density of 38.0 nC/m lies along the line y = -15.0 cm, between the points with coordinates x = 0 and x = 40.0 cm. Find the electric field's direction(counterclockwise from the +x axis). Magnitude=2597.3524601974621608226617005484 is Correct
An infinitely long uniform line charge of 20 nC/m lie along the z axis in free...
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...
6. Consider a line charge with uniform charge density λ lying on the x-axis from z...
6. Consider a line charge with uniform charge density λ lying on the x-axis from z =-L to 0. a) Determine the electric field a distance y above the right end of the line charge (point P in the figure) and a distance r to the right of the line charge (point P2 in the figure). P2 b) In lecture you saw the electric field of an infinite line charge. Now we will consider a "semi-infinite" line charge; that is,...
1. An infinite line of uniform positive charge runs along the x axis and has a...
1. An infinite line of uniform positive charge runs along the x axis and has a line charge density of λ=20.8 m nC . Consider the point (0 m, 2.00 m) which is located 2.00 meters above the infinite line. What is the magnitude of the electric field at this point? 2. An infinite horizontal plane of uniform negative charge sits at a height ofz=0. For a point at a height of z=−3m (i.e., 3 meters below the infinite plane),...
ANSWER ALL PARTS Problem 1. (30 points) Consider a line with uniform charge density io along...
ANSWER ALL PARTS
Problem 1. (30 points) Consider a line with uniform charge density io along a z-axis that extends from in the diagram below a to- u, as seen 2a As found in the previous exam, the algebraic form of the electric potential along the z axis is (a) we want to expand this electric potential function as an infinite series for the case when a. However, the logarithm function is not amenable to a binomial expansion, so we...
Starting from Coulomb's law in integral form in terms of the charge density and a volume integration, calculate the electric field at the origin of coordinates for a uniform line charge density λ that extends from (x,y,z) = (R,0,0) to (0,R,0) along an arc of radius R. 4.
2. A line of charge with uniform density of 38.0 nC/m lies along the line y 12.0 cm between the points x 5.0 cm and 40.0 cm. Calculate the electric field (both the magnitude and direction) at the origin due to this charge distribution. (2436 N/C, 137.9°)
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
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...
6. Consider a line charge with uniform charge density λ lying on the x-axis from z =-L to 0. a) Determine the electric field a distance y above the right end of the line charge (point P in the figure) and a distance r to the right of the line charge (point P2 in the figure). P2 b) In lecture you saw the electric field of an infinite line charge. Now we will consider a "semi-infinite" line charge; that is,...
ANSWER ALL PARTS
Problem 1. (30 points) Consider a line with uniform charge density io along a z-axis that extends from in the diagram below a to- u, as seen 2a As found in the previous exam, the algebraic form of the electric potential along the z axis is (a) we want to expand this electric potential function as an infinite series for the case when a. However, the logarithm function is not amenable to a binomial expansion, so we...
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