Kathmandu University
Dhulikhel, Nepal
PHYS102 (Assignment-3)
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1)​ Calculate the work done by a force field 𝐹 = (𝑧𝑥 + 𝑦) 𝑖 + (𝑥 − 𝑦) 𝑗 along
2
the path (0,0) to (2,1) following the parabola 𝑥 = 4𝑦
2)​ Find the surface area of the sphere of radius R.
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2
3)​ Evaluate the flux of 𝐹 = (𝑥 , 2𝑥𝑦, 𝑧) through the surface of the box
defined by 0 ≤ 𝑥 ≤ 2, 0 ≤ 𝑦 ≤ 3, 0 ≤ 𝑧 ≤ 4,
4)​Verify
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Gauss
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divergence
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𝐹 = 𝑥𝑖 + 𝑦𝑗 + 𝑧𝑘
over
theorem
a
unit
using
cube
the
defined
vector
by
the
field
limits
0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1, 0 ≤ 𝑧 ≤ 1
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5)​ Consider the vector field 𝐹 = 𝑦𝑖 − 𝑥𝑗 over the surface bounded by a unit
circle in the xy-plane. Verify Stokes theorem.