Question

, At one point in space, the direction of the electric field ctor is given in the Cartesian systen by the unit vector E = 1N51-2N5j . 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 at this point? What is the direction angle OE of the electric field vector at this point?

Answer 1

The scalar components of the electric field vector can be found by multiplying the magnitude of the field by the respective components of the unit vector. The direction angle is found by taking the arctan of the ratio of Ey to Ex.

Step-by-step explanation:

To determine the scalar components Ex, Ey, and Ez of the electric field vector E at a given point, and the direction angle θE of the electric field vector, we start by acknowledging the provided unit vector  = 1/√√51 - 2/√√5Â. The magnitude of the electric field vector is given as E = 400.0 V/m. It follows that we need to multiply each component of the unit vector by the magnitude to get the respective scalar components. Hence, Ex = E * (1/√√5) = 400.0 * (1/√√5) V/m and Ey = E * (-2/√√5) = 400.0 * (-2/√√5) V/m. Because no z-component is given, we assume Ez = 0 V/m.

The direction angle can be found by calculating the inverse tangent of the ratio of Ey to Ex, taking into account the sign to ensure the angle is in the correct quadrant.