Calculating electric field at a certain point in space

[tobywashere]

Homework Statement

Two small charges, +6.0 x 10^-5C and -2.0x10^-5C, are placed 36 cm apart. Calculate the magnitude of the electric field at a point 18 cm above the midpoint of the line joining the two charges, on the perpendicular to that line (and thus equidistant from the charges).

Homework Equations

E = kq / r²

The Attempt at a Solution

The three charges form a triangle with length 36 cm as the base and height 18 cm. The distance between the two charges is 36 cm. The distance from any of the charges to the point in space is approximately 18*sqrt[2], or 25.5 cm (using pythagorean theorem).
Therefore, the electric field exerted by the first charge is
k(6.0x10^-5)/(0.255)²
= 8333333 N/C [45 degrees above the horizontal]
The electric field exerted by the second charge is
k(2.0x10^-5)/(0.255)²
= 2777777 N/C [45 degrees below the horizontal]
The net electric field is the sum of these two fields. Since they form right angles to each other, we can use pythagorean theorem
E² = 8333333² + 2777777²
E = 8.8x10⁶
Using tan inverse, the angle of the resultant electric field is 27 degrees above the horizontal.
However, the textbook says that the answer should be 6.6x10⁶N/C
The textbook isn't always right, so am I right or is the textbook right this time?

 

[Abhishekdas]

Hi tobywashere...i do get the same thing as you got...and i did not even look at your solution... i tried it myself...got the same answer as you got and i saw that you have done the same thing...Sure looks like the book is wrong... I would like to see what answer some other PF members get ...

 

[tobywashere]

Yeah I'm pretty sure the textbook is wrong. Thanks!

 

[Abhishekdas]

Welcome...