Calculating electric field at a certain point in space

AI Thread Summary
Two charges, +6.0 x 10^-5 C and -2.0 x 10^-5 C, are positioned 36 cm apart, and the electric field is calculated at a point 18 cm above their midpoint. Using the formula E = kq / r², the electric fields from each charge are computed to be approximately 8.33 x 10^6 N/C and 2.78 x 10^6 N/C, respectively. The net electric field is found to be about 8.8 x 10^6 N/C at an angle of 27 degrees above the horizontal. However, this result contradicts the textbook's answer of 6.6 x 10^6 N/C, leading to a consensus among participants that the textbook may be incorrect. The discussion highlights the importance of verifying calculations in physics problems.
tobywashere
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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?
 
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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 ...
 
Yeah I'm pretty sure the textbook is wrong. Thanks!
 
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