The electric field in a certain region is acting radially outward and is given by E = Ar where r is the distance from origin and A is constant. The charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by :

Figure given shows four arrangement of charged particles, all at the same distance from the origin. Rank the situations according to the net electric potentials (V₁, V₂, V₃, V₄) at the origin, most positive first :-

Consider a conducting spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field  and the electric potential V(r) with the distance r from the centre, is best represented by the graph (Here dotted line represents potential curve and bold line represents electric field curve) :-

Two point charge of 100 mC and –4 mC are positioned at points (–2√3, 3√3, –4) and (4√3, –5√3, 6) respectively of a Cartesian coordinate system. Find the force vector on the –4 µC charge? All the coordinates are in meters.

The electric field in a  region is given by  N/C for x < 0. A closed cylinder of length 2m and cross-section area 10² m² is kept in such a way that the axis of cylinder is along x-axis and its centre coincides with origin. The total charge inside the cylinder is : 

[Take : ε₀ = 8.85 × 10^–12 C²/N–m²]

A sphere of radius R carries charge density proportional to the square of the distance from the center: ρ = Ar², where A is a positive constant. At a distance of R/2 from the center, the magnitude of the electric field is :-

A particle of mass m, charge –Q is constrained to move along the axis of a ring of radius a. The ring carries a uniform charge density + λ along its circumference. Initially, the particle lies in the plane of the ring at a point where no net force acts on it. The period of oscillation of the particle when it is displaced slightly from its equilibrium position is -

The surface charge density of a thin charged disc of radius R is s. The value of the electric field at the centre of the disc is  . With respect to the field at the centre, the electric field along the axis at a distance √3R from the centre of the disc :

Three charges -q, +q and +q are situated in X-Y plane at points (0, -a), (0, 0) and (0, a) respectively.  The potential at a distant point r (r >> a) in a direction making an angle θ from the Y-axis :-

A proton and an α-particle are initially at a distance 'r' apart. Find the KE of α-particle at a large separation from proton after being released :-