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...

 

[rwisz]

As a scientist, it is important to first check your calculations and make sure they are accurate. It seems that you have made a small error in your calculation for the distance from the charges to the point in space. Using the Pythagorean theorem, the distance should be approximately 25.9 cm, not 25.5 cm. This small difference may account for the discrepancy between your answer and the textbook's answer.

Additionally, it is important to consider the units in your calculations. The electric field is typically measured in units of N/C, not just N. So your final answer should be 8.8x106 N/C, not just 8.8x106.

Overall, your approach to solving the problem seems correct and it is always good to double check your work and consider the units in your calculations. It is also important to keep in mind that there may be slight differences in answers due to rounding or slight variations in the problem. As a scientist, it is important to be open to different interpretations and always strive for accuracy in your calculations.