Engineering Electromagnetics, W. H. Hayt and J. A. Buck, McGraw Hill, 2001 (6th edition) 2장 족보

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Engineering Electromagnetics, W. H. Hayt and J. A. Buck, McGraw Hill, 2001 (6th edition) 연습문제 풀이 2장 풀이.

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2.1. Four 10nC positive charges are located in the z = 0 plane at the corners of a square 8cm on a side.
A fifth 10nC positive charge is located at a point 8cm distant from the other charges. Calculate the
magnitude of the total force on this fifth charge for
=
0:
Arrange the charges in the xy plane at locations (4,4), (4,-4), (-4,4), and (-4,-4). Then the fifth charge
will be on the z axis at location z = 4
√
2, which puts it at 8cm distance from the other four. By
symmetry, the force on the fifth charge will be z-directed, and will be four times the z component of
force produced by each of the four other charges.
F =
4 √
2
× q2
4π
0d2 =
4 √
2
× (10−8)2
4π(8.85 × 10−12)(0.08)2 = 4.0 × 10−4 N
2.2. Two point charges of Q1 coulombs each are located at (0,0,1) and (0,0,-1). (a) Determine the locus
of the possible positions of a third charge Q2 where Q2 may be any positive or negative value, such
that the total field E = 0 at (0,1,0):
The total field at (0,1,0) from the two Q1 charges (where both are positive) will be
E1(0, 1, 0) =
2Q1
4π
0R2 cos 45◦ ay = Q1
4
√
2π
0
ay
where R =
√
2. To cancel this field, Q2 must be placed on the y axis at positions y > 1 if Q2 > 0,
and at positions y < 1 if Q2 < 0. In either case the field from Q2 will be

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