In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x²^y² + yz³ - 2z³^x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0). A) 4.3 V/m B) 2.0 V/m C) -8.1 V/m D) 8.6 V/m E) 74 V/m

Question

Quizplus · Accepted Answer

To find the electric field vector, we need to take the gradient of the electric potential function. The gradient operator is: ∇ = î(∂/∂x) + ĵ(∂/∂y) + k^(∂/∂z) Taking the gradient of the electric potential function V(x,y,z), we get: ∇V = (3²^y²)î + (3²^x² + z³)ĵ + (-2³^x + 3yz³)k^ Now we can substitute the given values of (x,y,z)=(1.0,1.0,1.0) into this expression to get the electric field vector at that point: E = - ∇V = - (3î + 1ĵ -5k^) Taking the magnitude of E, we get: |E| = √(3^2 + 1^2 + (-5)^2) = 8.6 V/m Therefore, the correct answer is D) 8.6 V/m.

In a Certain Region,the Electric Potential Due to a Charge