1. If D = 4x°dx – 2zāy + 2yā, C/m², find the following: a. V• D b. the total charge lying within the region –1< x,y,z < 1 2. Calculate the divergence of D = (÷)[10xyzd, + 5x²zãy + (2z³ – 5x²y)ãz] at P(-2,3,5). 3. Find the electric flux density at a point having a distance 4 m from a uniform line charge of 6 nC/m lying along the z axis in free space. (10 4. Let D* = y²z³dz + 2xyz³ dy + 3xy²z² âz pC/m² in free space. a. Find the total electric flux passing through the surface x = 5, 0 < y < 1, 0< z3 2 in a direction away from the origin. 5. An electric field is given as Ē = -10e (sin2zåx + xsin2zāy + 2xcos2zaz)V/m a. Find E at P(5,0,). %3D b. How much work is done in moving a charge of 2nC an incremental distance of 1 mm from P in the direction of åy? äy? đ,? đx + ảy + ả,? 6. Given the electric field Ē = (y + 1)ảx + (x – 1)ãy + 2ãz, find the potential difference between the points а. (2, —2, —1) аnd (0,0,0) b. (3,2, —1) апd (-2, -3,4) 7. Five equal point charges, Q = 20nC, are located at x = 2,3, 4, 5, 6 m. Find the potential at the origin.
1. If D = 4x°dx – 2zāy + 2yā, C/m², find the following: a. V• D b. the total charge lying within the region –1< x,y,z < 1 2. Calculate the divergence of D = (÷)[10xyzd, + 5x²zãy + (2z³ – 5x²y)ãz] at P(-2,3,5). 3. Find the electric flux density at a point having a distance 4 m from a uniform line charge of 6 nC/m lying along the z axis in free space. (10 4. Let D* = y²z³dz + 2xyz³ dy + 3xy²z² âz pC/m² in free space. a. Find the total electric flux passing through the surface x = 5, 0 < y < 1, 0< z3 2 in a direction away from the origin. 5. An electric field is given as Ē = -10e (sin2zåx + xsin2zāy + 2xcos2zaz)V/m a. Find E at P(5,0,). %3D b. How much work is done in moving a charge of 2nC an incremental distance of 1 mm from P in the direction of åy? äy? đ,? đx + ảy + ả,? 6. Given the electric field Ē = (y + 1)ảx + (x – 1)ãy + 2ãz, find the potential difference between the points а. (2, —2, —1) аnd (0,0,0) b. (3,2, —1) апd (-2, -3,4) 7. Five equal point charges, Q = 20nC, are located at x = 2,3, 4, 5, 6 m. Find the potential at the origin.
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