Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 2, Problem 2.1P

Three point charges of equal magnitude q, that will yield a zero net electric field at the origin.

Expert Solution & Answer
Check Mark
To determine

The coordinates of fourth point charge.

Answer to Problem 2.1P

The fourth point charge is at (1.19,1.19).

Explanation of Solution

Given Information:

The magnitude of all four point charges is q. Three charges are at x=2 , y=+2 and y=2 . The total electric field at origin is zero.

Calculation:

The electric field at origin due to first point charge,

   E1=q4πε0 ( 2 )2a^x =q16πε0a^x

The electric field at origin due to second point charge,

   E2=q4πε0 ( 2 )2(a ^y) =q16πε0a^y

The electric field at origin due to third point charge,

   E3=q4πε0(2)a^y =q8πε0a^y

Let E4 be the electric field due to fourth point charge. Then,

   E1+E2+E3+E4=0(q 16π ε 0 a ^x)+(q 16π ε 0 a ^y)+(q 8π ε 0 a ^y)+E4=0 q16πε0(a ^x+a ^y)+E4=0 E4=q16πε0(a ^x+a ^y) =q4πε0(4)(a ^xa ^y) =q4πε0( 4/ 2 )(1 2 a ^x1 2 a ^y) r2=4/2=22 r=1.68

From this calculation, the x coordinate and y coordinate are equal to positive sign. The distance of this point from origin is 1.68. So, the position of fourth point charge is,

   =( 1.68 2 , 1.68 2 )=(1.19,1.19)

Conclusion:

The fourth point charge is at (1.19,1.19).

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Engineering Electromagnetics

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