1000 identical drops of mercury are charged to a potential of \(1 \text{V}\) each. They coalesce to form a single drop, the potential of this new drop will be
The potential of a coalesced drop is related to the individual potential by \(V' = n^{2/3} V\). For \(n = 1000\), \(V' = (1000)^{2/3} \times 1 = 100 \text{V}\).
A point charge is placed at origin. Assuming potential to be zero at infinity, potential difference at two point A and B is found to be 10 V i.e., \(V_A – V_B = 10 \text{V}\). Now if the reference at infinity is changed to 10 V, then \(V_A – V_B\) will be
The potential difference between two points is independent of the reference level of potential because the change in reference shifts both potentials by the same constant value.
If electric potential (in volt) in a region is expressed as \(V(x, y, z) = 2xy – yz\), the electric field (in N/C) at point \((1, 0, 1)\text{ m}\) will be equal to
Using \(\vec{E} = -\left(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k}\right)\), we get \(E_x = -2y\), \(E_y = z - 2x\), and \(E_z = y\). Substituting \((1, 0, 1)\), we get \(vec{E} = -\hat{j}\).
Two charged spherical conductors of radii \( R_1 \) and \( R_2 \) (\( R_1 > R_2 \)) have equal surface charge densities placed at large distance from each other. If they are connected by a conducting wire, then
The potential of a sphere with surface charge density \( \sigma \) is \( V = \frac{\sigma R}{\varepsilon_0} \). Since \( R_1 > R_2 \), \( V_1 > V_2 \). Charge flows from higher potential (larger sphere) to lower potential (smaller sphere).