The electric potential in a region is represented as
`V=2x+3y-z`
obtain expression for electric field strength.

Explanation

To find the expression for the electric field strength given the electric potential \( V = 2x + 3y - z \), we can follow these steps:

### Step 1: Understand the relationship between electric potential and electric field
The electric field \( \vec{E} \) is related to the electric potential \( V \) by the equation:
\[ \vec{E} = -\nabla V \]
where \( \nabla V \) is the gradient of the potential.

### Step 2: Calculate the gradient of the potential
The gradient in three dimensions is given by:
\[ \nabla V = \left( \frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}, \frac{\partial V}{\partial z} \right) \]

### Step 3: Differentiate \( V \) with respect to \( x \)
We differentiate \( V \) with respect to \( x \):
\[ \frac{\partial V}{\partial x} = \frac{\partial}{\partial x}(2x + 3y - z) = 2 \]

### Step 4: Differentiate \( V \) with respect to \( y \)
Next, we differentiate \( V \) with respect to \( y \):
\[ \frac{\partial V}{\partial y} = \frac{\partial}{\partial y}(2x + 3y - z) = 3 \]

### Step 5: Differentiate \( V \) with respect to \( z \)
Now, we differentiate \( V \) with respect to \( z \):
\[ \frac{\partial V}{\partial z} = \frac{\partial}{\partial z}(2x + 3y - z) = -1 \]

### Step 6: Combine the results to find the electric field
Now we can substitute these results into the expression for the electric field:
\[ \vec{E} = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k} \right) \]
Substituting the values we calculated:
\[ \vec{E} = -\left( 2 \hat{i} + 3 \hat{j} - 1 \hat{k} \right) \]
This simplifies to:
\[ \vec{E} = -2 \hat{i} - 3 \hat{j} + 1 \hat{k} \]

### Final Expression for Electric Field
Thus, the expression for the electric field strength is:
\[ \vec{E} = -2 \hat{i} - 3 \hat{j} + 1 \hat{k} \]

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