Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is $\lambda$. [This question includes concepts from 12th syllabus]

1. $\frac{2k\lambda }{r}$

2. $\frac{k\lambda }{r}$

3. $\frac{k\lambda }{2r}$

4. $\frac{k\lambda }{4r}$

The electrostatic field due to a charged conductor just outside the conductor is:

In the absence of other conductors, the surface charge density

(1) Is proportional to the charge on the conductor and its surface area

(2) Inversely proportional to the charge and directly proportional to the surface area

(3) Directly proportional to the charge and inversely proportional to the surface area

(4) Inversely proportional to the charge and the surface area

Two identical conductors of copper and aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminum will be 

(1) Zero

(2) Greater than in copper

(3) Equal to that in copper

(4) Less than in copper

Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is 

(1) F

(2) 3F/4

(3) F/2

(4) F/4

The figure shows the electric lines of force emerging from a charged body. If the electric fields at A and B are E_A and E_B respectively and if the distance between A and B is r, then:

1. \(E_{A}~>~E _{B}\)
2. \(E_{A}~<~E _{B}\)
3. \(E_{A}~=~\frac{E_{B}}{r^{}}\)
4. \(E_{A}~=~\frac{E_{B}}{r^{2}}\)

\(ABC\) is an equilateral triangle. Charges \(+q\)  are placed at each corner. The electric intensity at \(O\) will be: 

       
1. \(\frac{1}{4\pi\epsilon _0}\frac{q}{r^{2}}\)
2. \(\frac{1}{4\pi\epsilon _0}\frac{q}{r^{}}\)
3. zero
4. \(\frac{1}{4\pi\epsilon _0}\frac{3q}{r^{2}}\)

The magnitude of electric field intensity E is such that, an electron placed in it would experience an electrical force equal to its weight is given by 

(1) mge

(2) $\frac{mg}{e}$

(3) $\frac{e}{mg}$

(4) $\frac{e^2}{m^2}g$

A charge particle is free to move in an electric field. It will travel 

(1) Always along a line of force

(2) Along a line of force, if its initial velocity is zero

(3) Along a line of force, if it has some initial velocity in the direction of an acute angle with the line of force

(4) None of the above

An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like 

(1) A

(2) B

(3) C

(4) D