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 E\vec{E} can be obtained through the sum of horizontal component Eh\vec{E}_h and vertical component Ev\vec{E}_v through the Pythagorean theorem:

E=Eh2+Ev2=152+212=25.8N/C.E = \sqrt{E_h^2+E_v^2} = \sqrt{15^2+21^2} = 25.8\,\mathrm{N/C}.

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

cosθ=EhE=1525.8  θ=54.5.\cos\theta = \dfrac{E_h}{E} = \dfrac{15}{25.8} \, \Rightarrow \; \theta = 54.5^\circ.


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