Electric Charge...

Find the force experienced by a semicircular rod having a charge q as shown in figure. Radius of the wire is R, and the line of charge with linear charge density $$\lambda$$ passes through its center and is perpendicular to the plane of wire.

One-fourth of a sphere of radius R is removed as shown in Fig. An electric field E exists parallel to the xy plane. Find the flux through the remaining curved part :

Two identical particles are charged and held at a distance of $$1 m$$ from each other. They are found to be attracting each other with a force of $$0.027 N$$. Now, they are connected by a conducting wire so that charge flows between them. When the charge flow stops, they are found to be repelling each other with a force of $$0.009 N$$. Find the initial charge on each particle :

Two similarly and equally charged identical metal spheres A and B repel each other with a force of $$2 \times 10^{-5} N$$. A third identical uncharged sphere C is touched with A and then placed at the midpoint between A and B. Find the net electric force on C :

Find the electric field vector at P(a, a, a) due to three infinitely long lines of charges along the x-, y- and z-axes, respectively. The charge density, i.e., charge per unit length of each wire is $$\lambda$$ :

A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring is q, and the linear charge density on the straight wire is $$\lambda$$. The interaction force between the ring and the wire is :

A conic surface is placed in a uniform electric field E as shown in Fig. such that the field is perpendicular to the surface on the side AB. The base of the cone is of radius R, and the height of the cone is h. The angle of the cone is $$\theta  $$. Find the magnitude of the flux that enters the cone's curved surface from the left side. Do not count the outgoing flux $$(\theta  < 45^{\circ})$$ :

A charge $$Q$$ is divided into two charges $$q$$ and $$Q-q$$. The value of $$q$$ such that the force between them is maximum, is :

In a region, the intensity of an electric field is given by $$E = 2i + 3j + k$$ in $$NC^{-1}$$. The electric flux through a surface $$S = 10i \ m^{2}$$ in the region is:

The spatial distribution of the electric field due to two charges (A, B) is shown in figure. Which one of the following statements is correct ?