Emag Final

7/28/2019 Emag Final

http://slidepdf.com/reader/full/emag-final 1/5

I. Identifications.1. The two main indicators of the manner in which a vector field changes form point topoint throughout space are ______ and ________.2. When the divergence of a vector field is _________, that region is said to containsources or _________.3. A region that contains positive charges contains _________ of ψ. The _________ of

the electric flux density D will be positive in this region.4. The ___________ of a vector flux density A is the outflow of flux from a small closedsurface per unit volume as the volume shrinks to zero.5. ___________, ____, originates on positive charge and terminates on negativecharge. In the absence of negative charge, the flux terminates at _________.6. _________ of electric charge gives rise to one coulomb of electric flux.7. _________ states that the total flux out of a closed surface is equal to the net chargewithin the surface.8. State Maxwell’s First Equation / Divergence Theorem. 9. The ____ operator is defined only in cartesian coordinates.

10. Coulomb stated that the ________ between 2 very small objects separatedin a vacuum or _________ by a distance which is large compared to their size is

________ to the square of the distance between them.11. The units of the various charge densities ρL, ρS, and ρV are _____, ______,and _____.12. _______ is the amount of charge that is transferred through the cross – section of a wire in 1 s when there is a current of 1 A in the wire.13. What are the various forms of charge distributions? _______________ 14. _______ It constitutes the source of all electromagnetic fields.15. The vector force on a unit positive charge is called _________.16. The unit C

2 / N. m 2 and N / C are dimensionally equal to _____ and ______.17. The forced expressed by Coulomb’s Law is a mutual force, for if we multiplyQ 1, by a factor n, the force on Q2 is also _______ by the same factor n.

18. It is also true that the force on a charge in the presence of several other charges is the _______ of the forces on that charge due to each of other chargesacting alone.19. The constant ε0 is called the ________ and has the magnitude measured in

_______.20. List some electrical component that can be mathematically modeled as a linecharge, as a surface charge, and as the volume charge distributions.

__________ __________ __________

II. Problem Solving ( Round off all your answers to three decimal places )

1. Find the distance between (1, π / 4, 0 ) and ( 1, 3π / 4, π ), where the pointsare given in spherical coordinates.

2. Two point charges Q 1 = 550 μC and Q 2 = - 700 μC are located at ( -3,0,0 ) mand ( 0,0,3 ) m, respectively. Find the force on Q 2.



3. Find E at the origin if the following charge contributions are present in freespace: point charge, 12 nC, at N( 2,0,6 ); a uniform surface charge density, 0.2nC / m

2at x = 2; a uniform line charge density, 3 nC / m at x = - 2, y = 3.

4. Find the net charge enclosed in a cube 2 m on an edge, parallel to the axes

and centered at the origin, if the charge density isρ = 50 z 2 cos ( ¼ π y ) μC / m 3 1. Evaluate both sides of the divergence theorem for the field ( choose one )

a. D = 2xy a X + x 2 a Y C / m 2 and the rectangular parallelepiped formed by x =

0 and 1, y = 0 and 2, and z = 0 and 3.

b. D = 5 r 2 a r C / m 2 and for the volume enclosed by r = 4 m and θ = π / 4.

c. D = 10 ρ 3 a ρ C / m 2 and for the volume enclosed by ρ= 1 m, ρ = 2 m, z = 0,

and z = 10 m.

2. Find ∇. A

a. at ( 2, 2, 0 ) for A = √ (x 2 + y 2 ) a X

b. at ( 0.5, π / 4, π / 4 ) for A = 5 sin θ a θ+ 5 sin φ a φ

3. Charge in the form of a plane sheet with density equal to 40 μC / m 2 is located at z =

- 0.5 m. A uniform line charge of density equal to – 6 μC / m lies along the y axis. Whatnet flux crosses the surface of a cube 2 m on an edge, centered at the origin.

4. A point charge, Q = 30 nC, is located at the origin in cartesian coordinates. Find theelectric flux density D at ( 1, 3, - 4 )m.

5. Three point charges Q1 = 30 nC, Q2 = 150 nC, and Q3 = - 70 nC, are enclosed by

surface S. What net flux crosses S?

6. Given D = 10 x a x C / m 2 , determine the flux crossing a 1 - m 2 area that is normal tothe x – axis at x = 3 m.

Given the electric field E = ( 4 x − 2 y)a x − ( 2 x + 4 y)a y , find:

a) the equation of the streamline that passes through the point P( 2 , 3 ,−4 ): We write



b) a unit vector specifying the direction of E at Q( 3 ,−2 , 5 ):

2.28 If E = 20e−5 y(cos 5 xa x − sin 5 xay), find:

a) |E| at P(π/ 6 , 0.1 , 2 ):

b) a unit vector in the direction of E P , c) the equation of the direction line passing through P



3.5. Let D = 4 xya x + 2(x2 + z 2 )a y + 4 yz a z C / m2 and evaluate surface integrals to find the total

charge enclosed in the rectangular parallelepiped 0 < x < 2, 0 < y < 3, 0 < z < 5 m.

The cylindrical surface ρ = 8 cm contains the surface charge density, ρ s = 5e−20| z | nC / m2.

a) What is the total amount of charge present?



b) How much flux leaves the surface ρ = 8 cm, 1 cm < z < 5cm, 30o < φ < 90o?

Emag Final

Documents

Transcript of Emag Final