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Find the charge density
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- Find the electric field a distance z above the midpoint of a straight line segment of length 2L, which carries a uniform line charge A.arrow_forwardConsider a hollow sphere of radii h and 3h, interior and exterior respectively. The charge density on the sphere is ρ=ar, C/m3, where a is a positive constant, and r is the distance from the center of the sphere to an arbitrary point inside the sphere. A point charge with charge Q, of magnitude −16πah4 C, is located at the center of the sphere. Find the electric field, Eux, of the distribution, sphere and point charge, at a point (P), on the x-axis, located at a distance of 2h, measured with respect to the center of the sphere. In this case consider that ah2= 4. Use k=9×109, ux unit vector in the x-direction, π=3.14arrow_forwardFind the electric field of a distance z above the midpoint of a straight line segment of length 2 L, which carries a uniform line charge A.arrow_forward
- An ideal uniformly charged ring is situated on the xy-plane withits center at the origin. Assuming that the charge of the ring is negative,a proton moving in the +z -axis going to the origin willarrow_forwardcalculate the flux of the vector field through the given surface. ~F= (x2−2)~i through a square of side length 3 in the yz-plane, oriented in the negative x-direction.arrow_forwardFor problem 7, calculate the total flux through the one side of the cube in kNm2/C for a particle with a charge 3.39 uC at the center of the cube.(5 sig. figs.)arrow_forward
- Consider a closed surface S fully enclosing the point charge Q. Which of the following is true about the net electric flux through S?arrow_forwardIn Fig-1, there are two infinite planes A and B, parallel to the YZ plane. Their surface charge densities are σA = −47nC/m2 and σB = 28nC/m2. The separation between the planes A and B is d = 10m. a) Now, we place a conducting spherical shell of radius R=0.1d in between the planes. The spherical shell conductor carries a surface charge density σ = −25μC/m2. The coordinates of the center(d/2,d/2,0), P1 (4d/5, d/2, 0) and P2 (d/2, d/4, 0). Find the net electric field at points P1 and P2 in unit vector notation.arrow_forwardFind the electric field at a distance h from the center of a ring of radius R, whose linear charge density is homogeneous and equal to λarrow_forward
- A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.arrow_forwardIf a closed cylindrical surface of height 0.3 m and diameter 0.2 m were placed as shown, completely enclosing q1 and q3, what would be the net flux through the surface due to all three charges?arrow_forwardTwo hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position r⃗ due to the point charge is: E⃗ (r⃗ )=C/r^2 r^ where C is a constant proportional to the charge, r=|r⃗ |, and r^=r⃗ /r is the unit vector in the radial direction. What is the electric flux Φ3 through the annular ring, surface 3, the flux Φ1 through surface 1, and flux Φ2 passing outward through surface 2?arrow_forward
