Subjects electromagnetism

Current Continuity

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Current Continuity


1. The term $\frac{\partial \rho_V}{\partial t}$ represents the rate of change of the volume charge density $\rho_V$ at a point with respect to time. This means statement (a) is correct. 2. The current continuity equation expresses the principle of conservation of electric charge, stating that charge cannot be created or destroyed. Hence, statement (b) is correct. 3. For a capacitor, if one plate has charge $Q$, the other plate must have charge $-Q$ to maintain overall charge neutrality. So, statement (c) is correct. 4. The differential form of the current continuity equation is given by: $$\nabla \cdot \mathbf{J} = -\frac{\partial \rho_V}{\partial t}$$ where $\mathbf{J}$ is the current density vector. Note the negative sign, which means statement (d) is incorrect as it misses the negative sign. 5. The current continuity equation holds in all cases, including static cases where the time derivative of charge density is zero. Therefore, statement (e) is incorrect. Final correct statements are (a), (b), and (c).