Physics 351 Electricity and Magnetism Test1 Prof. Asim Gangopadhyaya I will not divulge any information about this exam to any one for any reason. Name 1) The integral ~a ≡ Z S d~a is sometimes called the vector area of the surface S. Use problem 60 a to show that ~a = 0 for any closed surface. problem 60a : •Z V ± ~ ∇ T ¶ d 3 r = I S T d ~ S ‚ . 2) Find the surface integral [ H ~v · d~a ] of the vector ﬁeld ~v = r 2 sin θ ˆ r + 4 r 2 cos θ ˆ θ + r 2 tan θ ˆ φ over a closed surface formed by an inverted hemispherical bowl of radius R h x 2 + y 2 + z 2 = R 2 i resting on the xy
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