Answer to Question #207193 in Electric Circuits for Hafee

Question #207193

Calculate the electric field at one corner off a square 80𝑐𝑚 on a side if the other three corners are occupied by charges each of magnitude 18.2 x 10-4C.


1
Expert's answer
2021-06-15T15:11:26-0400

Side of square, a = 80 cm=80×102 m80\space cm=80\times10^{-2}\space m

Electric field due to horizontally placed charge, E1=kqa2=(9×109)(18.2×104)(80×102)2E_1=\dfrac{kq}{a^2}=\dfrac{(9\times10^9)(18.2\times10^{-4})}{(80\times10^{-2})^2}

E1=2.0475×109 N/C(left)E_1=2.0475\times10^{9}\space N/C(left)


Electric field due to vertically placed charge, E2=2.0475×109 N/C(downward)E_2=2.0475\times10^{9}\space N/C(downward)

Eres1=E12+E22+2E1E2cos90°=3.50×109 N/C(diagonally)E_{res_1}=\sqrt{E_1^2+E_2^2+2E_1E_2\cos90\degree}=3.50\times10^9\space N/C(diagonally)


Electric field due to diagonally placed charge, E3=(9×109)(18.2×104)(802×102)2E_3=\dfrac{(9\times10^9)(18.2\times10^{-4})}{(80\sqrt{2}\times10^{-2})^2}

E3=1.447×109 N/CE_3=1.447\times10^{9}\space N/C


Eres=Eres1+E3=4.94×109 N/C(diagonally)E_{res}=E_{res_1}+E_3=4.94\times10^{9}\space N/C(diagonally)


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