Q1 a) Express the vector field H = xyz ax + xyz ay + xyz az...

    

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Q1 a) Express the vector field H = xy²z ax + x²yz ay + xyz² az in cylindrical coordinate and determine H at (3,-4, 5) b) Let A = 2xy ax + xz ay-y az. Evaluate A dv over a cylindrical region p ≤ 3,0 ≤z≤5 c) Evaluate the divergence and curl for the given vector F = pz² cost ap + zsin² az d) If F = x² ax + y² ay +(2² - 1) az, find J. F.ds, where S is defined by p = 2, 0 <z<2,0 ≤ ≤2T e) Calculate the total outward flux of vector F = p² sin ap + z cos ao + pz a Q2 a) The finite sheet 0 ≤ x ≤ 1,0 ≤ y ≤ 1 on he z = 0 plane has a charge density ps = xy(x² + y² + 25,³¹² nC/m². Find (i) The total charge on the sheet (ii) The total electric field at (0, 0, 5) (iii) The force experienced by a -1mC charge located at (0,0,5) Q1 a) Express the vector field H = xy²z ax + x²yz ay + xyz² az in cylindrical coordinate and determine H at (3,-4, 5) b) Let A = 2xy ax + xz ay-y az. Evaluate A dv over a cylindrical region p ≤ 3,0 ≤z≤5 c) Evaluate the divergence and curl for the given vector F = pz² cost ap + zsin² az d) If F = x² ax + y² ay +(2² - 1) az, find J. F.ds, where S is defined by p = 2, 0 <z<2,0 ≤ ≤2T e) Calculate the total outward flux of vector F = p² sin ap + z cos ao + pz a Q2 a) The finite sheet 0 ≤ x ≤ 1,0 ≤ y ≤ 1 on he z = 0 plane has a charge density ps = xy(x² + y² + 25,³¹² nC/m². Find (i) The total charge on the sheet (ii) The total electric field at (0, 0, 5) (iii) The force experienced by a -1mC charge located at (0,0,5)

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Express the vector field H xyz ax xyz ay xyz az in cylindrical coordinate and determine H at 34 5 The vector field H is expressed as H xyz ax xyz ay xyz az The value of H at 3 4 5 is H 3 4 5 ax 3 4 5 ... View the full answer