Question

Given the potential field (V=5⋅x³.y−7.z)V/m, find the electric flux density in C/m² at the point P:(1,3,10).

please note that the electric permitivity in free space ε=8.85×10⁻¹².
please only enter the x-component.
please put you answer in the exponential format (1.88e−9,−2.13e−8, and so on) (without spaces)

Answer 1

To find the electric flux density at the point P:(1,3,10), we need to calculate the electric field intensity by taking the negative gradient of the given potential field. Substituting the values into the electric field expression, we can then find the electric flux density by multiplying the electric field intensity by the electric permitivity in free space.

Step-by-step explanation:

To find the electric flux density at the point P:(1,3,10), we can use the formula D = ε * E, where D is the electric flux density, ε is the electric permitivity in free space, and E is the electric field intensity.

Given the potential field V=5⋅x³.y−7.z V/m, we can find the electric field intensity by taking the negative gradient of the potential field. Taking the gradient, we get E = (15⋅x².y)î + (-7)ĵ, where î and ĵ are unit vectors in the x and y directions respectively.

Substituting the values x=1 and y=3 into the electric field expression, we get E = 15.ĵ - 7.ĵ = 8.ĵ V/m. Finally, substituting the values ε=8.85×10⁻¹² and E=8.ĵ into the formula for electric flux density, we get D = ε * E = (8.85×10⁻¹²)(8) = 7.08×10⁻¹¹ C/m².