Which of the following integrals will give the correct value of the total flux passing through the rectangular surface lying on the plane = 100°, defined by the intervals 2
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![Which of the following integrals will give the correct value of the total flux passing through the rectangular surface lying on the plane = 100°, defined by the intervals 2 <p<5 m and 1
<z< 2 m, given the electric field in the region is D = 02zap + 20z aq + 2po2 V/m?
100 T
2sin
180
z dp dz
,2 .5
100 T
2sin
pz dp dz
180
100 T
pz dp dz
180
100 T
2.
180
z dp dz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F901383ca-2272-4433-aadf-68fffa7d4bdc%2Ffb815998-b8c1-431e-9418-130b5fd1c2e4%2Fhfkwlyv_processed.jpeg&w=3840&q=75)
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- An infinite cylinder of radius R has a charge density given by p(r) = ar", where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) 7€or satisfies V ·Ē = 0 for r > R. Explain briefly why this condition must be obeyed.If D = (2y + z)a, + 4xya, + xa, C/m², find %3D (a) The volume charge density at (-1, 0, 3) (b) The flux through the cube defined by 0 s xs 1,0 sys1,0szs1 (c) The total charge enclosed by the cubeA 2D annulus (thick ring) has an inner radius Ri and outer radius Ro, and charge Q non-uniformlydistributed over its surface. The 2D charge density varies with radius r by η(r)=Cr 4 for Ri ≤ r ≤ Roand η=0 for all other r. C is a constant. Answer the following in terms of the variables given above. Note: Gauss' Law will not be useful here.a) Find an expression for C such that the total charge of the annulus is Q. Include the SI units for C next to your answer.Do the units make sense?b) Draw a clear picture and use it to set up the integral to calculate the E-field at a point on the axis of the annulus (this axis is perpendicular to the plane of the annulus) a distance z from the center of the annulus. *** You must complete all the steps short of computing the integral (i.e. your eventual answer must be an integral with only ONE variable of integration and all other variables constant.) Show that your answer has the correct SI units for the electric field.
- For this question, Figure 2 (see image). Consider the electric field of a disk of radius R and surface charge density σ along the z-axis as: (see image) a) Use this expression to find the electric field of the disk very close to the disk i.e. Z << R such that the disk looks like an infinite plane with surface charge density σ. b) Use a Gaussian cylinder (pill box) to find the electric field of the plate at this limit (Z << R such that the disk looks like an infinite plane), and compare it with your answer from part a.An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aRT E(r) : 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.In free space, let D = 8xyz4ax + 4x2z4ay + 16x2yz3 az pC/m2.Find the total electric flux passing through the rectangularsurface z = 2, 0 < x < 2, 1 < y < 3, in the az direction. Find Eat P(2, −1, 3).
- An electric field of magnitude 464 V/m passing through a flat square plate of length 0.644 m on a side makes an angle of 63.6 degrees with the surface of plate. Determine the electric flux passing through the surface of the square plate. (Hint: the angle given here is the angle that the field makes with the surface, not with the area vector. In what direction does the area vector of a surface point relative to that surface?)The figure below shows a disk of radius 0.50 m is oriented with its normal unit vector în making an angle 0 to uniform electric field E with magnitude 10. x 103 N/C. The electric flux is calculated to be 2.0 x 103 N-m²/C. What is the angle 0 that this disk normal unit vector în makes with the electric field E in r = 0.50m 0 = ? E O 75° 65° none of the given choices O 60° 80°Problem 2.01. Three plates with surface charge density |o| = 8.85 μC/mm² are stacked on top of each other. The top and bottom plates have charge density to while the center plate has charge density -0. (a) Find the magnitude and direction of the electric field between the plates. (b) Find the magnitude and direction of the electric field above and below the plate stack.
- We have the electric field: E = 5xx + 2y + (4/π)z. (a) Calculate its flow through the three surfaces S1, S2, S3 of the figure. The S3 measure is the fourth of the surface area of a unit radius and center that coincides with the beginning of the axes. (b) If there are no loads in the space, calculate the flow of E from the curvilinear surface. (ni, x, y, z are unit vectors)Consider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to λ this line of charge is given by E= 2kef= -, where is a unit vector directed radially outward Σπερμ from the infinitely long wire of charge. Hint #3 a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A,ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation 3 V(r) = b. There is a reason we are not setting V(r → ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(ro), with our current…Find the flux of F = xi - 2yj + zk across the portion of cylinder x² + z² = 9 in the first and forth octants. (3,-3,0) n X (0,0,3) (3,0,0) (0,3,0) y