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Two uniform electric fields are superimposed at a point: E1 = 14 N/C pointing along the positive x-axis, and E2 = 7.0 N/C pointing along the positive y-axis. At what angle above the positive x-axis will a positive test charge accelerate?
A27 degrees
B45 degrees
C63 degrees
D90 degrees
Answer & Solution
Correct answer: A. 27 degrees
1. A positive test charge accelerates in the same direction as the combined electric field.
2. The combined field has an x-component of 14 N/C and a y-component of 7.0 N/C.
3. The angle above the x-axis is arctan(7.0 / 14) = arctan(0.5) = 26.6 degrees, which rounds to 27 degrees.
4. Assuming the two equal-looking numbers give a 45-degree angle, as in option B, only works when both components are equal, which they are not here.
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.3 Electric Field_
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