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Emag Exam

The document provides a set of five problems related to electric flux, electric fields, charge densities, magnetic fields, and current densities. Each problem requires calculations involving point charges, uniform charge distributions, and vector forces. The document includes relevant formulas for solving these problems.

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AlisaHeracles
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32 views1 page

Emag Exam

The document provides a set of five problems related to electric flux, electric fields, charge densities, magnetic fields, and current densities. Each problem requires calculations involving point charges, uniform charge distributions, and vector forces. The document includes relevant formulas for solving these problems.

Uploaded by

AlisaHeracles
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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NAME: ________________________________________

INSTRUCTION: Answer any 4 out of 5 of the following items. Make a separate sheet for all
your answers and separate sheets for your solutions. Thanks and God bless everyone. (Note: Don’t
forget to write your names on all pages. Be careful with term like vector and with dot and cross
products).

1. Calculate the total electric flux leaving the cubical surface formed by the six planes x, y, z = ±5
1
if the charge distribution is: (a) two point charges, 0.1 μC at (1, −2, 3) and 7 μC at (−1, 2, −2);
(b) a uniform line charge of π μC/m at x = −2, y = 3; (c) a uniform surface charge of 0.1 μC/m2
on the plane y = 3x.

2. In free space, let D = 8xyz4ax + 4x2z4ay + 16x2yz3 az pC/m2. (a) Find the total electric flux
passing through the rectangular surface z = 2, 0<x<2, 1<y< 3, in the az direction. (b) Find E
at P(2, −1, 3). (c) Find an approximate value for the total charge contained in an incremental
sphere located at P (2, −1, 3) and having a volume of 10−12 m3.

3. Determine an expression for the volume charge density associated with each D field: (a) D =
4𝑥𝑦 2𝑥 2 2𝑥 2 𝑦
ax + ay − az ; (b) D = zsinϕaρ + zcosϕaϕ + ρsinϕaz; (c) D = sinθsinϕar + cosθsinϕaθ
𝑧 𝑧 𝑧2
+ cosϕaϕ.

4. The field B = −2ax + 3ay + 4az mT is present in free space. Find the vector force exerted on a
straight wire carrying 12 A in the aAB direction, given A(1,1,1) and: (a) B(2,1,1); (b) B(3,5,6).

5. Current density is given in cylindrical coordinates as J = −106z1.5az A/m2 in the region 0≤ρ≤20
μm; for ρ≥20 μm, J =0. (a) Find the total current crossing the surface z = 0.1 m in the az
direction. (b) If the charge velocity is 2×106 m/s at z = 0.1 m, find ρv there. (c) If the volume
charge density at z = 0.15 m is −2000 C/m3, find the charge velocity there.

Formulas:
𝑄𝑒𝑛𝑐
Φ𝐸 = ; 𝑄𝑒𝑛𝑐 = 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑐ℎ𝑎𝑟𝑔𝑒𝑠 (𝑓𝑜𝑟 𝑛𝑢𝑚 1)
𝜖𝑂

𝐷𝜌 𝜕𝐷 𝜕𝐷𝑦 𝜕𝐷𝑧
Ψ = ∬𝑆 𝐷𝑍 𝑑𝑥𝑑𝑦 ; 𝐸𝜌 = ; 𝑄Δ𝑉 = ( 𝜕𝑥𝑥 + + ) × Δ𝑉
𝜖𝑂 𝜕𝑦 𝜕𝑧

𝜕𝐷 𝜕𝐷𝑦 𝜕𝐷𝑧 1 𝜕 1 𝜕𝐷𝜙 𝜕𝐷𝑧 1 𝜕


𝑑𝑖𝑣 𝐷 = ( 𝜕𝑥𝑥 + + ); 𝑑𝑖𝑣 𝐷 = 𝜌 𝜕𝜌 (𝜌𝐷𝜌) + 𝜌 + ; 𝑑𝑖𝑣 𝐷 = 𝑟 2 𝜕𝑟 (𝑟 2 𝐷𝑟 ) +
𝜕𝑦 𝜕𝑧 𝜕𝜙 𝜕𝑧
1 𝜕 1 𝜕𝐷𝜙
(𝑠𝑖𝑛𝜃𝐷𝜃 ) + 𝑟𝑠𝑖𝑛𝜃
𝑟𝑠𝑖𝑛𝜃 𝜕𝜃 𝜕𝜙

F = 𝐼L × B; 𝐼L = 𝐼 ∙ ⃗⃗⃗⃗⃗
𝐴𝐵

𝐼 = ∫𝑆 𝐽 ∙ 𝑑𝑆; 𝑑𝑆 = 𝜌𝑑𝜙𝑑𝜌 𝑎̂𝜌 ; 𝐽 = 𝜌𝑣 𝑣

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