at point p(x,y,z) electric field of E1=-7i-6j+8k E2=6i+3j+7k E3=3i-4j-6k Are mea

Question

at point p(x,y,z) electric field of E1=-7i-6j+8k E2=6i+3j+7k E3=3i-4j-6k Are measured and plotted A. What principle can we use to find the total electric fieldat point p? B. Find the magnitude and direction of Etotal atP(x,y,z). C. Find the force acting on a point charge q=5nC placed atpoint P. at point p(x,y,z) electric field of E1=-7i-6j+8k E2=6i+3j+7k E3=3i-4j-6k Are measured and plotted A. What principle can we use to find the total electric fieldat point p? B. Find the magnitude and direction of Etotal atP(x,y,z). C. Find the force acting on a point charge q=5nC placed atpoint P.

Explanation / Answer

(a) principle is superposition. Thetotal E field is just the sum of the individual E fields. . (b) Total E field is   (-7 + 6 + 3)i + (-6 + 3 - 4)j + (8 + 7 -6)k =  2i - 7j + 9k . Magnitudeis   (22 + 72 +92 )1/2 =   11.576 N/C (Iassume the E field is given in SI units) . Direction? with respect to what? This is a poorly wordedquestion. When asking for direction, a reference must always bespecfied, e.g. "find the angle the E field makes with the positivex axis" or something like that. Just asking for "direction"by itself has no meaning. . But I will ASSUME you need the direction with respect to eachaxis. . angle E field makes with x axis = arccos (4/11.576) =   69.78degrees . angle E field makes with y axis = arccos(-7/11.576) =   127.21degrees . angle E field makes with z axis = arccos (9/11.576) =   38.97degrees . (c) force = qE = 5 x10-9 * ( 2i - 7j + 9k) =   (10i - 35j + 45k) x 10-9 Newtons

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