Question

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 ?.

Answer 1

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

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