1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
An infinitely long uniform line charge distribution of charge per unit length $$\lambda$$ lies parallel to the y-axis in the y-z plane at $$z = {{\sqrt 3 } \over 2}$$a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is $${{\lambda L} \over {n{\varepsilon _0}}}$$ ($${{\varepsilon _0}}$$ = permittivity of free space), then the value of n is

2
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0

An infinitely long solid cylinder of radius R has a uniform volume charge density $$\rho$$. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression $${{23\rho R} \over {16k{\varepsilon _0}}}$$. The value of k is _____________.

3
IIT-JEE 2011 Paper 1 Offline
Numerical
+3
-0

Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The surface tension of the soap film is $$\gamma$$. The system of charges and planar film are in equilibrium, and $$a = k{\left[ {{{{q^2}} \over \gamma }} \right]^{1/N}}$$, where k is a constant. Then N is __________.

4
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1

A solid sphere of radius R has a charge Q distributed in its volume with a charge density $$\rho = K{r^a}$$, where K and a are constants and r is the distance from its centre. If the electric field at $$r = R/2$$ is 1/8 times than at $$r = R$$, find the value of $$a$$.