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A line charge with charge density
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Fundamentals Of Electromagnetics With Justask! Set
- The electric potential V in a region of space is given by V(x,y,z)=A(x^2−3y^2+z^2)where A is a constant. Derive an expression for the electric field E→ at any point in this region. The work done by the field when a 1.50-μC test charge moves from the point (x,y,z)=(0,0,0.250m) to the origin is measured to be 6.00×10−5J. Determine A. Determine the electric field at the point (0, 0, 0.250 m). Show that in every plane parallel to the xz-plane the equipotential contours are circles.arrow_forwardDetermine the magnitude of the Electric Field Intensity at the origin given the following charge distributions in free space: point charge, 7 nC at P(2, 0, 3); uniform infinite line charge, 3 nC/m at x = -2, y = 5; uniform surface charge density, 0.8 nC/m^2 at x = 4. Use k = 9 x 10^9.arrow_forwardFind E at the origin if the following charge distributions are present in free space: point charge, 12 nC at P(2, 0, 6); uniform line charge density, 3nC/m at x =−2, y = 3; uniform surface charge density, 0.2nC/m² at x = 2arrow_forward
- Find the electric potential difference V12 between two points in free space at radial distances r1and r2 from an infinite line of charge with density ρl along the z-axis,where the electric field due to an infinite line of charge is: ~E= ˆrρl/2e0rarrow_forwardA point charge of -3.00 micro Coulomb is located in the center of a spherical cavity of radius 6.50 cm that, in turn, is at the center of an insulating charged solid sphere. The charge density in the solid is 7.35 x 10-4 C/m3. Calculate the electric field (in N/C) inside the solid at a distance of 9.50 cm from the center of the cavity. (Don't express your answers in scientific notation)arrow_forwardAn infinitely long uniform line charge is located at y = 3, z = 5 if ρL = 30nC/m, find E at: (a) the origin; (b) PB(0,6,1); (c) PC(5,6,1).arrow_forward
- Within the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3 . (i) Find an expression for electric field intensity for region r < 8 cm. Hence, calculate the electric field intensity at a point having rectangular coordinates of (x, y, z) = ( 3 cm, 2cm, 0 ). (ii) Assume that all of the electric charge is removed from a spherical region centered at (x, y, z) =(3 cm, 0, 0) and having a radius of 1 cm. Calculate the total electric field intensity at point (x,y,z) = (3 cm, 2 cm, 0).arrow_forwardA cylindrical metal can has a height of 27 cm and a radius of 11 cm. the electric field is directed outward along the entire surface of the can (including the top and bottom), with a uniform magnitude of 4.0 x 105 N/C. How much charge does the can contain? 2. An insulating sphere with a radius of 20 cm carries a uniform volume charge density of 1.5 x 10-6 C/m3. Find the magnitude of the electric field at a point inside the sphere that lies 8.0 cm from the center. 3. A square metal plate with a thickness of 1.5 cm has no net charge and is placed in a region of uniform electric field 8.0 x 104 N/C directed perpendicularly to the plate. Find the resulting surface charge density on each face of the plate.arrow_forwardGiven a 2.215 nC/m2 surface charge at z = – 15. Solve E on point (250, 100, 10) caused by the surface charge in (nC/m).arrow_forward
- A 5C point charge is placed 5m above a perfect conductor surface in xy plane extending to infinity in both dimensions find the total electric field everywhere.arrow_forwardA point charge, QA = 1μC is at A(0, 0, 1), and QB = −1μC is at B(0, 0, −1).Find Er, Eθ and E∅ at P(2, 3, 1).arrow_forwardCalculate D in rectangular coordinates at point P(2,-3,6) produce by: (a) a point charge QA=55 mC at Q(-2,3,-6); (b) a uniform line charge ρLB=20mCmρLB=20mCm on the x axis; (c) a uniform surface charge density ρSC=120μCm2ρSC=120μCm2on the plane z=-5m.arrow_forward
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