Question

In a certain region of space the electric potential is given by V=+Ax²y−Bxy². where A = 5.00 V/m³ and B = 8.00 V/m³.

A) Calculate the magnitude of the electric field at the point in the region that has coordinates x = 2.50 mm, y = 0.400 mm, and z = 0.

Answer 1

To calculate the magnitude of the electric field at a given point, we can use the relationship between electric potential and electric field. To find the magnitude of the electric field, we need to calculate the derivatives of the electric potential with respect to x, y, and z components, and then substitute the given values into the equations. Finally, we can calculate the magnitude of the electric field using the formula for vector magnitude.

Step-by-step explanation:

To calculate the magnitude of the electric field at a given point, we can use the relationship between electric potential and electric field. The electric field, E, at a point is the negative gradient of the electric potential, V. In this case, the electric potential is given as V = +Ax²y - Bxy².

To calculate the electric field at a specific point (x, y, z), we need to find the derivatives of V with respect to x, y, and z components. Then, we substitute the given values into the electric field equation. The electric field at the given point can be found using the formulas:

E_x = -dV/dx, E_y = -dV/dy, E_z = -dV/dz.

Finally, we can calculate the magnitude of the electric field using the formula:

|E| = sqrt(E_x² + E_y² + E_z²).