Electrostatic Potential and Capacitance

Two charged thin infinite plane sheets of uniform surface charge density σ+and σ−, where |σ+| > |σ−|, intersect at right angle. Which of the following best represents the electric field lines for this system.

A two point charges 4q and –q are fixed on the x-axis at x = −d/2 and x = d/2, respectively. If a third point charge ' q ' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will:

Two small spherical balls of mass 10 g each with charges -2μC and 2μC, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of 100μC/m² such that length of rod makes an angle of 30° with electric field generated by charge sheet. Net torque acting on the rod is: (Take ε? = 8.85 × 10?¹²C²/Nm²)

Effective capacitance of parallel combination of two capacitors $C_1$ ${}_{}$ and ${}_{}$ $C_2$ is $10\mu \mathrm{F}$ $$ . When these capacitor are individually connected to a voltage source $1\mathrm{V}$ of $1\mathrm{V}$ $$ , the energy stored in the capacitor $C_2$ ${}_{}$ is 4 times that of ${}_{}$ $C_1$ . If these capacitors are connected in series, their effective capacitance will be

In finding the electric field using Gauss law the formula $\left|\stackrel{?}{E}\right|=\frac{q_{\text{enc}}}{{\epsilon }_0\left|A\right|}$ $\stackrel{}{}\frac{{}_{}}{{}_{}}$ is applicable. In the formula ${\epsilon }_0$ ${}_{}$ is permittivity of free space, $A$ $$ is the area of Gaussain surface and $q_{\text{enc}}$ ${}_{}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? Only when the Gaussian surface is an

Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.

27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is……… times that of a smaller drop.

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:

(m = mass of charged particle)

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ……………. V.