mcq div curl.docx

Vector Calculus

Multiple Choice Quizzes 1.

2.

3.

4.

5.

Find the divergence of the vector field

Find the curl of

Given that F and G are vector fields and f is a scalar field, which of the following statements is false?

Given that

, which of the following statements is false?

Use Green’s Theorem to find the work done by the force field in moving a particle once in a counter clockwise

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direction around the circle of radius “a” centred at the origin.

6. Use Green’s Theorem to evaluate

for C: boundary of the region

lying between the graphs of

7. Use the Divergence Theorem to calculate the flux field

of the vector

out of the sphere S with equation

8. Use the Divergence Theorem to calculate the flux

of the vector field

out of the surface S of the region

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9.

Use Stokes's Theorem to evaluate where triangle with vertices (2, 0, 0), (0, 1, 0), and (0, 0, 4) . 6

around the

-2 -6 2

10 .

Use Stokes’s Theorem to evaluate

where

and S

is the surface of the paraboloid

11 .

Let S be an imaginary closed surface in an ideal fluid which bounds a domain D. The conservation of mass states that the rate of change of the mass of fluid in D equals the rate at which fluid enters D across S. Given that the mass changes at rate

(where

rate at which mass is flowing out D across S is follows that:

is the density)and the ,it

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12 .

13 .

Given the vector field where , k is a scalar constant, s is a constant vector, and r ¹ s, which of the following statements is not correct?

Suppose a closed surface S bounds a region R in which charge is distributed with density ρ. Given that the electric field E due to the charge satisfies div E = kρ, and the total charge in R is Q, find the total flux of E out of R through S. kρQ kQ πk²Q πkQ

14 .

For the cylindrical coordinate system, the coordinate r-curves are vertical straight lines. horizontal straight half-lines radiating from the z-axis. horizontal straight lines. horizontal circles with centres on the z-axis.

15 .

Find the gradient of the scalar field coordinates.

in terms of the cylindrical