ERB.EE.BEF22903 1

BEF 22903

ENGINEERING ELECTROMAGNETICS

TUTORIAL 1

1. The charges on the charged plastic rod can be transferred to a metal sphere by

conduction or induction technique. Explain both techniques. 2. Briefly explain on the conservation of electric charged.

3. State and explain Coulomb’s Law.

4. Point charges Q1 = 5 µC and Q2 = -4 µC are placed at (3, 2, 1 ) and (-4, 0, 6),

respectively. Determine the force on Q1.

(Ans: -1.8291 x - 0.5226 y +1.3065 z mN)

5. Point charges Q1 and Q2 are, respectively, located at (4, 0, -3) and (2, 0, 1). If Q2 = 4

nC, find Q1 such that

(a) The Er

at (5, 0, 6) has no z-component. (b) The force on a test charge at (5, 0, 6) has no x-component.

(Ans: (a) -8.3232 nC, (b) -44.945 nC)

6. Three surface charge distributions are located in free space as follows: 10 µC/m2 at

y = 2, -20 µC/m2 at y = -3, and 30 µC/m2 at y = -5. Determine Er

at (a) P(5, -1, 4) (b) R(0, -4, 1) (c) Q(3, 4, -5)

(Ans: (a) 0 V/m, (b) 2.258 x 106 y V/m, (c) 1.13 x 10 6 y V/m)

7. A uniform line charge density of 10 nC/m is positioned at x = 0, y = 2, while another

uniform line charge density of -10 nC/m is positioned at x = 0, y = -2. Find Er

at the origin.

(Ans: -180 y V/m )

8. Infinite uniform line charges of 5 nC/m lie along the (positive and negative) x and y

axes in free space. Find Er

at: (a) PA(0, 0, 4); (b) PB(0, 3, 4).

(Ans: (a) 45 z V/m, (b) 10.8 y + 36.9 z V/m)

9. An infinite uniform line charge ρL = 2 nC/m lies along the x-axis in free space, while point charge of 8 nC each are located at (0, 0, 1) and (0, 0, -1).

(a) Find Er

at (2, 3, -4).

(b) To what value should ρL be changed to cause Er

to be a zero at (0, 0, 3)?

(Ans:(a) 2.008 x + 7.325 y V/m, (b) -3.75 nC/m)

10. A uniform line charge of 2µC/m is located on the z - axis. Find in rectangular coordinates at P(1, 2, 3) if the charge exists from: (a) -∞ < z < ∞ (b) -4 ≤ z ≤ 4

(Ans: (a) 7.2 x + 14.4 y kV/m, (b) 4.9 x + 9.8 y + 4.9 z kV/m)

ERB.EE.BEF22903 2

11. A ring placed along the y2 + z2 = 4, x = 0 carries a uniform charge 5 µC/m.

(a) Find Dr

at P(3, 0, 0). (b) If two identical point charges Q are placed at (0, -3, 0) and (0, 3, 0) in addition to

the ring, find the value of Q such that Dr

= 0 at P. (Ans: (a) 0.32 x µC/m2, (b)-51.182 µC )

12. A spherical charge distribution is given by

<<

=

otherwise

rrv

,0

41,mC/m10 3

2ρ

(a) Find the net flux crossing surface r = 2 m and r = 6 m.

(b) Determine Dr

at r = 5 m.

(Ans: (a) 125.7 mC, 377 mC (b) 1.2 r mC/m2)

13. A spherical charge distribution is given by

>

<=

ar

ara

ro

v

,0

,mC/m3

ρρ

Find Er

everywhere.

(Ans: mV/mˆ4

0

0

2

ra

rE

ε

ρ=

r, mV/mˆ

40

2

0

3

rr

aE

ε

ρ=

r )

14. Two point charges Q1 = 2 nC and Q2 = -4 nC are located at (1, 0, 3) and (-2, 1, 5),

respectively. Determine the potential at P(1, -2, 3). (Ans: 1.32V)

15. Three point charges Q1 = 1mC, Q2 = -2 mC, and Q3 = 3 mC are, respectively, located

at (0, 0, 4), (-2, 5, 1), and (3, -4, 6). (a) Find the potential Vp at P(-1, 1, 2). (b) Calculate the potential difference VPQ if Q is (1, 2, 3).

(Ans: (a) 3 x 106 V, (b) 0.69 x 106 V)