Answer to Question #146875 in Astronomy | Astrophysics for f

Question #146875
If the Horizontal component of the electric filed at 15 N/C and vertical component is 21 N/C find the direction (θ) of resultant electric ?.
1
Expert's answer
2020-11-27T14:00:35-0500

The total electric field "\\vec{E}" can be obtained through the sum of horizontal component "\\vec{E}_h" and vertical component "\\vec{E}_v" through the Pythagorean theorem:

"E = \\sqrt{E_h^2+E_v^2} = \\sqrt{15^2+21^2} = 25.8\\,\\mathrm{N\/C}."

Let "\\theta" be the angle between horizontal and the direction of the electric field. Therefore

"\\cos\\theta = \\dfrac{E_h}{E} = \\dfrac{15}{25.8} \\, \\Rightarrow \\; \\theta = 54.5^\\circ."


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