Question

the electric potential in a region of space varies as v=by/(a² + y²) . part a determine the components of e⃗ . express your answers in terms of the variables a , b , and y separated by commas..

Answer 1

To find the components of the electric field, take the negative gradient of the electric potential and differentiate it with respect to each variable.

Step-by-step explanation:

The electric field, E, can be determined by taking the negative gradient of the electric potential, V. This means taking the partial derivative of V with respect to each variable (a, b, and y) to find the corresponding components of E.

Ex = -∂V/∂x = 0

Ey = -∂V/∂y = -b(a² - y²)/(a² + y²)²

Ez = -∂V/∂z = 0

So the components of E are Ex = 0, Ey = -b(a² - y²)/(a² + y²)², and Ez = 0.