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Calculation of Electric Field at the Center of a Square Charge Configuration, Exercises of Electrical Engineering

The calculation of the electric fields ex and ey at the center of a square charge configuration, consisting of charges at the corners. The net fields are found using coulomb's law and the magnitudes and directions are determined. Useful for students studying electrostatics and electric fields.

Typology: Exercises

2011/2012

Uploaded on 07/20/2012

apurva
apurva 🇮🇳

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13. We choose the coordinate axes as shown on the diagram below. At the center of the square, the electric
fields produced by the charges at the lower left and upper right corners are both along the xaxis and
each points away from the center and toward the charge that produces it. Since each charge is a distance
d=√2a/2=a/√2 away from the center, the net field due to these two charges is
Ex=1
4πε02q
a2/2−q
a2/2=1
4πε0
q
a2/2
=8.99 ×109N·m2/C21.0×10−8C
(0.050 m)2/2=7.19 ×104N/C.
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d
d
a
a
x
y
−q
q−2q
2q
At the center of the square, the field produced by the charges at the upper left and lower right corners
are both along the yaxis and each points away from the charge that produces it. The net field produced
at the center by these charges is
Ey=1
4πε02q
a2/2−q
a2/2=1
4πε0
q
a2/2=7.19 ×104N/C.
The magnitude of the field is
E=E2
x+E2
y=2(7.19 ×104N/C)2=1.02 ×105N/C
and the angle it makes with the xaxis is
θ=tan
−1Ey
Ex
=tan
−1(1) = 45◦.
It is upward in the diagram, from the center of the square toward the center of the upper side.
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Partial preview of the text

Download Calculation of Electric Field at the Center of a Square Charge Configuration and more Exercises Electrical Engineering in PDF only on Docsity!

13. We choose the coordinate axes as shown on the diagram below. At the center of the square, the electric

fields produced by the charges at the lower left and upper right corners are both along the x axis and

each points away from the center and toward the charge that produces it. Since each charge is a distance

d =

2 a/2 = a/

2away from the center, the net field due to these two charges is

E

x

2 q

a

q

a

q

a

8. 99 × 10

N·m

/C

1. 0 × 10

C

(0.050 m)

= 7. 19 × 10

N/C.

d

d

a

a

x

y

−q

q

− 2 q

2 q

At the center of the square, the field produced by the charges at the upper left and lower right corners

are both along the y axis and each points away from the charge that produces it. The net field produced

at the center by these charges is

E

y

[

2 q

a

q

a

]

q

a

= 7. 19 × 10

N/C.

The magnitude of the field is

E =

E

x

+ E

y

2(7. 19 × 10

N/C)

= 1. 02 × 10

N/C

and the angle it makes with the x axis is

θ = tan

E

y

E

x

= tan

It is upward in the diagram, from the center of the square toward the center of the upper side.

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