Question

At one point in space, the direction of the electric field vector is given in the Cartesian system by the unit vector ˆE=1/√5ˆi−2/√5ˆj. If the magnitude of the electric field vector is E = 400.0 V/m, what are the scalar components Ex, Ey, and Ez of the electric field vector →E at this point? What is the direction angle θE of the electric field vector at this point?

a) Ex = 80.0 V/m, Ey = -160.0 V/m, Ez = 0 V/m, θE = 243.4°
b) Ex = -80.0 V/m, Ey = 160.0 V/m, Ez = 0 V/m, θE = 116.6°
c) Ex = 100.0 V/m, Ey = -200.0 V/m, Ez = 0 V/m, θE = 243.4°
d) Ex = -100.0 V/m, Ey = 200.0 V/m, Ez = 0 V/m, θE = 116.6°

Answer 1

The scalar components of the electric field vector at this point are Ex = 80.0 V/m, Ey = -160.0 V/m, and Ez = 0 V/m. The direction angle of the electric field vector is 243.4°.

Step-by-step explanation:

The scalar components of the electric field vector are Ex = 80.0 V/m, Ey = -160.0 V/m, and Ez = 0 V/m.

The direction angle of the electric field vector is given by the arctan(Ey/Ex).

Plugging in the values, we get θE = 243.4°.

Therefore, the correct option is a) Ex = 80.0 V/m, Ey = -160.0 V/m, Ez = 0 V/m, θE = 243.4°.