The electric field E = yi + xj represents a vector field where the components of the electric field vary with position in space.
Breaking it down:
- E is the electric field vector.
- i and j are unit vectors along the x-axis and y-axis, respectively.
- The field is given as:
- Eₓ = y (x-component depends on y)
- Eᵧ = x (y-component depends on x)
Key Interpretation:
- The electric field is non-uniform, meaning it changes from point to point.
- At different coordinates (x, y), the magnitude and direction of the field vary.
- This type of field shows cross-dependence, where:
- The x-component depends on the y-coordinate.
- The y-component depends on the x-coordinate.
Physical Insight:
- Such a field is typically used in problems involving:
- Field line analysis
- Divergence and curl calculations
- If you calculate:
- Divergence (∇·E) = ∂(y)/∂x + ∂(x)/∂y = 0 + 0 = 0
→ Indicates no net source or sink.
- Curl (∇×E) ≠ 0
→ The field has rotational characteristics.
Conclusion:
This electric field represents a position-dependent, rotational vector field with zero divergence, often used in theoretical electromagnetism problems.