The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge density ρ = A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant is:
A.
A Gaussian surface at distance r from centre.
At the centre of the sphere is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant is
As, Q = 2πAa2
i.e A = Q/2πa2
Two charges, each equal to q, are kept at x = −a and x = a on the x-axis. A particle of mass m and charge qo =-q/2 is placed at the origin. If charge qo is given a small displacement (y<< a) along the y-axis, the net force acting on the particle is proportional to
y
-y
1/y
1/y
A.
y
A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is
D.
A long cylindrical shell carries positive surface charge in the upper half and negative surface charge in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)
D.
Field lines should originate from a positive charge and terminate negative charge.
This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution, there is a finite value of the electric potential at the centre of the sphere, at the
surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.
Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qρ/3εo
Statement 2: The electric field at a distance r(r < R) from the centre of the sphere is ρr/3εo
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.
Statement 1 is true, Statement 2 is false
Statement 1 is false, Statement 2 is true
Statement 1 is false, Statement 2 is true
C.
Statement 1 is false, Statement 2 is true