Question
A long charged cylinder of linear charge density $+\lambda_1$ is surrounded by a hollow coaxial conducting cylinder of linear charge density $-\lambda_2$. Use Gauss’s law to obtain expressions for the electric field at a point (i) in the space between the cylinders, and (ii) outside the larger cylinder.

Answer

As Gauss’s Law states:$\oint\overrightarrow{E}.\vec{ds}=\frac{q}{\epsilon_0}$
  1. $\oint\overrightarrow{E_1}.\vec{ds}=\frac{\lambda_1l}{\epsilon_0}$
$\Longrightarrow\overrightarrow{E_1}=\frac{\lambda_1}{2\pi\epsilon_0r_1}\hat{r_1}$
  1. $\oint\overrightarrow{E_2}.\vec{ds}=\frac{(\lambda_1-\lambda_2)l}{\epsilon_0}$
$\Longrightarrow\overrightarrow{E_2}=\frac{(\lambda_1-\lambda_2)}{2\pi\epsilon_0r_2}\hat{r_2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

You are given two circuits as shown in Fig. 14.46, which consist of NAND gates. Identify the logic operation carried out by the two circuits.
  1.  
  1.  
Prove that the instantaneous rate of change of the activity of a radioactive substance is inversely proportional to the square of its half-life.
The string, the spring and the pulley shown in figure are light. Find the time period of the mass m.
A $60\mu F$ capacitor is connected to a $110V, 60Hz$ ac supply. Determine the rms value of the current in the circuit.
A galvanometer coil has a resistance of $12 \Omega$ and the metre shows full scale deflection for a current of $3 m$ A. How will you convert the metre into a voltmeter of range $0$ to $18 V$?
Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed w about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.
A mosquito is sitting on an $L.P.$ record disc rotating on a turn table at $33\frac{1}{3}$ revolutions per minute. The distance of the mosquito from the centre of the turn table is $10\ cm$. Show that the friction coefficient between the record and the mosquito is greater than $\frac{\pi^2}{81}.$ Take $g =10 m/s^2.$
A person looks at different trees in an open space with the following details. Arrange the trees in decreasing order of their apparent sizes.
Tree Height(m) Distance form the eye(m)
A 2.8 50
B 2.5 80
C 1.8 70
D 2.8 100

In the figure given below, a bar magnet moving towards the right or left induces an emf in the coils (1) and (2). Find, giving reason, the directions of the induced currents through the resistors AB and CD when the magnet is moving (a) towards the right, and (b) towards the left.
A certain material has refractive indices 1.56, 1.60 and 1.68 for red, yellow and violet light respectively.
  1. Calculate the dispersive power.
  2. Find the angular dispersion produced by a thin prism of angle 6° made of this material.