### Electric Potential and Electric Field CalculationIn a particular region of space, the electric potential \( V \) is given by the equation:\[ V = 9x - 4x^2 yz \]We need to determine the electric field \( \mathbf{E} \) in this region. The electric field components \( E_x \), \( E_y \), and \( E_z \) can be found using the relationship between the electric field and the electric potential:\[ \mathbf{E} = -\nabla V \]where \( \nabla V \) represents the gradient of the potential \( V \). The components of the electric field are given by:\[ E_x = -\frac{\partial V}{\partial x} \]\[ E_y = -\frac{\partial V}{\partial y} \]\[ E_z = -\frac{\partial V}{\partial z} \]Please calculate the x, y, and z components of the electric field vector \( \mathbf{E} \) using the equations provided.#### Hints- To calculate \( E_x \), take the partial derivative of \( V \) with respect to \( x \).- To calculate \( E_y \), take the partial derivative of \( V \) with respect to \( y \).- To calculate \( E_z \), take the partial derivative of \( V \) with respect to \( z \).Enter your answers in the spaces provided below:a. \( E_x = \) [ ____ ]b. \( E_y = \) [ ____ ]c. \( E_z = \) [ ____ ]

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In a particular region of space, the electric potential is given by V = 9x - 4x²yz. What is the electric field in the region? Give x, y, and components of the electric field vector E below. Hint a. E₂ = b. Ey = c. Ez =

In a particular region of space, the electric potential is given by V = 9x - 4x²yz. What is the electric field in the region? Give x, y, and components of the electric field vector E below. Hint a. E₂ = b. Ey = c. Ez =

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### Electric Potential and Electric Field Calculation

In a particular region of space, the electric potential \( V \) is given by the equation:

\[ V = 9x - 4x^2 yz \]

We need to determine the electric field \( \mathbf{E} \) in this region. The electric field components \( E_x \), \( E_y \), and \( E_z \) can be found using the relationship between the electric field and the electric potential:

\[ \mathbf{E} = -\nabla V \]

where \( \nabla V \) represents the gradient of the potential \( V \). The components of the electric field are given by:

\[ E_x = -\frac{\partial V}{\partial x} \]
\[ E_y = -\frac{\partial V}{\partial y} \]
\[ E_z = -\frac{\partial V}{\partial z} \]

Please calculate the x, y, and z components of the electric field vector \( \mathbf{E} \) using the equations provided.

#### Hints

- To calculate \( E_x \), take the partial derivative of \( V \) with respect to \( x \).
- To calculate \( E_y \), take the partial derivative of \( V \) with respect to \( y \).
- To calculate \( E_z \), take the partial derivative of \( V \) with respect to \( z \).

Enter your answers in the spaces provided below:

a. \( E_x = \) [ ____ ]

b. \( E_y = \) [ ____ ]

c. \( E_z = \) [ ____ ]

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