University of Windsor
Electrical and Computer Engineering
Pre_Lab Report
ELEC 2280 Electromagnetic Fields
Instructor: R. Rashidzadeh
Electrostatic Fields & Potential
Lab_2
1-Name: ______________________
Date: _______
ID:__________________________
Please answer the following questions.
1- For the finite line charge in Fig. 1 write an expression for the electric field.
Fig. 1
𝑝𝐿
(𝐸 = 4𝜋𝜖 𝑝 (−(𝑠𝑖𝑛𝛼2 − 𝑠𝑖𝑛𝛼1 ))𝛼𝑝 + (𝑐𝑜𝑠𝛼2 − 𝑐𝑜𝑠𝛼1 )𝛼𝑧 )
𝑜
2- What is the relationship between electric field and potential? For a given potential
V= f(x,y,z) how do you determine the electric field.
Given an electric potential, the electric field may be calculated as the negative of the
gradient of the potential. Assuming that the potential is given as 𝑉 = 𝑓(𝑥, 𝑦, 𝑧), the
electric field is determined by taking the partial derivatives with regard to each of
the spatial coordinates. Thus, the electrical field is
𝜕𝑣
𝜕𝑣
𝜕𝑣
𝐸 = − ( 𝑎𝑥 ,
𝑎𝑦 ,
𝑎 )
𝜕𝑥
𝜕𝑦
𝜕𝑧 𝑧
3- What is an electric dipole? Write an expression for electric potential and electric flux
density in the vacuum for a dipole at far-field.
An electric dipole is a combination of two charges of the same magnitude and
opposite charges which are a short distance apart. The dipole moment may be
defined as 𝑝 = 𝑄𝑑 , where Q represents the strength of the charge and 𝑑 is the
distance between the charges. When the distance between points of observation and
the dipole is large, that is, when the separation distance is significantly less than the
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𝑝𝑐𝑜𝑠𝜃
radial distance 𝑟 , the electric potential is provided by 𝑉 = 4𝜋𝑒 𝑟3. By getting the
𝑜
negative gradient of the potential, one can get the electric field. Having known the
electric field, the electric flux density 𝐷 is the result of multiplying the electric field
by 𝜖𝑜 . The resulting expression for the electric flux density is
4- Explain equipotential lines and plot equipotential lines for a point charge.
The lengthy lines depicting the equipotential lines of a point charge are the dashed
ones, whereas the ones depicting the electric field lines are the green ones.
Equipotential lines are consistently perpendicular (90 degrees) to the electric field
lines, and this results in them being circular in nature, surrounding the charge. The
𝑞
electric potential of a point charge is provided by 𝑉 = 4𝜋𝑒 𝑟 . This statement
𝑜
demonstrates that the electric potential is constant given a certain value of 𝑟 . Which
means no work is needed to get a charge to move along an equipotential line. But as
one approaches or recedes from the charge, the value 𝑟 changes, which acts on the
electric potential, correspondingly increasing or decreasing it.
The pre-lab report is individual and must be submitted separately before the Lab.
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