dimensional analysis

Question

The dimension of the quantity (1/2)ε₀E² (where ε₀ is the permittivity of free space and E is the electric field) is the same as that of:

RankGuru · Accepted Answer

1. **Identify the Physical Quantity**: The term $\frac{1}{2} \epsilon_0 E^2$ represents the **Energy Density** (energy stored per unit volume) in an electrostatic field.
2. **Derive Dimensions of Energy Density**:
   - Dimension of Energy: $[ML^2T^{-2}]$.
   - Dimension of Volume: $[L^3]$.
   - Dimension of Energy Density: $\frac{[ML^2T^{-2}]}{[L^3]} = [ML^{-1}T^{-2}]$.
3. **Analyze Options**:
   - **Energy**: $[ML^2T^{-2}]$.
   - **Force**: $[MLT^{-2}]$.
   - **Pressure**: $\frac{[Force]}{[Area]} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.
   - **Power**: $[ML^2T^{-3}]$.
4. **Conclusion**: The dimensions match those of **Pressure**.

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dimensional analysis

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