2012
JEE Mains
MCQ
AIEEE 2012
In a uniformly charged sphere of total charge $Q$ and radius $R,$ the electric field $E$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
A.
B.
C.
D.
2011
JEE Mains
MCQ
AIEEE 2011
Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d\left( {d < < 1} \right)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,
A.
$v\, \propto \,{x^{ - 1}}$
B.
$y\, \propto \,{x^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$
C.
$v\, \propto \,x$
D.
$v\, \propto \,{x^{ - {\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$
2011
JEE Mains
MCQ
AIEEE 2011
The electrostatic potential inside a charged spherical ball is given by $\phi = a{r^2} + b$ where $r$ is the distance from the center and $a,b$ are constants. Then the charge density inside the ball is:
A.
$ - 6a{\varepsilon _0}r$
B.
$ - 24\pi a{\varepsilon _0}$
C.
$ - 6a{\varepsilon _0}$
D.
$ - 24\pi {\varepsilon _0}r$
2010
JEE Mains
MCQ
AIEEE 2010
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30^ \circ }$ with each other. When suspended in a liquid of density $0.8g$ $c{m^{ - 3}},$ the angle remains the same. If density of the material of the sphere is $1.6$ $g$ $c{m^{ - 3}},$ the dielectric constant of the liquid is
A.
$4$
B.
$3$
C.
$2$
D.
$1$
2010
JEE Mains
MCQ
AIEEE 2010
A thin semi-circular ring of radius $r$ has a positive charges $q$ distributed uniformly over it. The net field $\overrightarrow E $ at the center $O$ is
A.
${q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
B.
$ - {q \over {4{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
C.
$ - {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
D.
$ {q \over {2{\pi ^2}{\varepsilon _0}{r^2}}}\,j$
2010
JEE Mains
MCQ
AIEEE 2010
Let there be a spherically symmetric charge distribution with charge density varying as $\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$ upto $r=R,$ and $\rho \left( r \right) = 0$ for $r>R,$ where $r$ is the distance from the erigin. The electric field at a distance $r\left( {r < R} \right)$ from the origin is given by
A.
${{{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$
B.
${{4\pi {\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 3} - {r \over R}} \right)$
C.
${{4{\rho _0}r} \over {4{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$
D.
${{{\rho _0}r} \over {3{\varepsilon _0}}}\left( {{5 \over 4} - {r \over R}} \right)$
2009
JEE Mains
MCQ
AIEEE 2009
Let $P\left( r \right) = {Q \over {\pi {R^4}}}r$ be the change density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $'p'$ inside the sphere at distance ${r_1}$ from the center of the sphere, the magnitude of electric field is :
A.
${Q \over {4\pi \,{ \in _0}\,r_1^2}}$
B.
${{Qr_1^2} \over {4\pi \,{ \in _0}\,{R^4}}}$
C.
${{Qr_1^2} \over {3\pi \,{ \in _0}\,{R^4}}}$
D.
$0$
2009
JEE Mains
MCQ
AIEEE 2009
A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:
A.
$-1$
B.
$1$
C.
$ - {1 \over {\sqrt 2 }}$
D.
$ - 2\sqrt 2 $
2009
JEE Mains
MCQ
AIEEE 2009
Two points $P$ and $Q$ are maintained at the potentials of $10$ $V$ and $-4$ $V$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is :
A.
$9.60 \times {10^{ - 17}}J$
B.
$ - 2.24 \times {10^{ - 16}}J$
C.
$ 2.24 \times {10^{ - 16}}J$
D.
$- 9.60 \times {10^{ - 17}}J$
2009
JEE Mains
MCQ
AIEEE 2009
(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)
Statement-1 : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q.$
Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.
A.
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
B.
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C.
Statement- 1 is false, Statement- 2 is true.
D.
Statement- 1 true, Statement- 2 is false
2008
JEE Mains
MCQ
AIEEE 2008
A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty ,$ where $r$ is the distance from the center of the shell?
A.
B.
c
c
C.
D.
2007
JEE Mains
MCQ
AIEEE 2007
Charges are placed on the vertices of a square as shown. Let $\overrightarrow E $ be the electric field and $V$ the potential at the center. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then
A.
$\overrightarrow E $ changes, $V$ remains unchanged
B.
$\overrightarrow E $ remains unchanged, $V$ changes
C.
both $\overrightarrow E $ and $V$ change
D.
$\overrightarrow E $ and $V$ remain unchanged
2007
JEE Mains
MCQ
AIEEE 2007
The potential at a point $x$ (measured in $\mu \,m$) due to some charges situated on the $x$-axis is given by $V\left( x \right) = 20/\left( {{x^2} - 4} \right)$ volt
The electric field $E$ at $x = 4\,\mu \,m$ is given by
The electric field $E$ at $x = 4\,\mu \,m$ is given by
A.
$(10/9)$ volt / $\mu $ $m$ and in the $ + ve$ $x$ direction
B.
$\left( {5/3} \right)$ volt/ $\mu $ $m$ and in the $-ve$ $x$ direction
C.
$\left( {5/3} \right)$ volt/$\mu $ $m$ and in the $+ve$ $x$ direction
D.
$\left( {10/9} \right)$ volt/ $\mu \,m$ and in the $-ve$ $x$ direction
2007
JEE Mains
MCQ
AIEEE 2007
An electric charge ${10^{ - 3}}\,\,\mu \,C$ is placed at the origin $(0,0)$ of $X-Y$ co-ordinate system. Two points $A$ and $B$ are situated at $\left( {\sqrt 2 ,\sqrt 2 } \right)$ and $\left( {2,0} \right)$ respectively. The potential difference between the points $A$ and $B$ will be
A.
$4.5$ volts
B.
$9$ volts
C.
zero
D.
$2$ volts
2006
JEE Mains
MCQ
AIEEE 2006
An electric dipole is placed at an angle of ${30^ \circ }$ to a non-uniform electric field. The dipole will experience
A.
a translation force only in the direction of the field
B.
a translation force only in a direction normal to the direction of the field
C.
a torque as well as a translational force
D.
a torque only
2006
JEE Mains
MCQ
AIEEE 2006
Two spherical conductors $A$ and $B$ of radii $1$ $mm$ and $2$ $mm$ are separated by a distance of $5$ $cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is
A.
$4:1$
B.
$1:2$
C.
$2:1$
D.
$1:4$
2006
JEE Mains
MCQ
AIEEE 2006
Two insulating plates are both uniformly charged in such a way that the potential difference between them is ${V_2} - {V_1} = 20\,V.$ (i.e., plate $2$ is at a higher potential). The plates are separated by $d=0.1$ $m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1.$ What is its speed when it hits plate $2$?
$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$
$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$
A.
$2.65 \times {10^6}\,m/s$
B.
$7.02 \times {10^{12}}\,m/s$
C.
$1.87 \times {10^6}\,m/s$
D.
$32 \times {10^{ - 19}}\,m/s$
2005
JEE Mains
MCQ
AIEEE 2005
A charged ball $B$ hangs from a silk thread $S,$ which makes angle $\theta $ with a large charged conducting sheet $P,$ as shown in the figure. The surface charge density $\sigma $ of the sheet is proportional to
f
f
A.
$\cot \,\theta $
B.
$\cos \,\theta $
C.
$\tan \,\theta $
D.
$\sin \,\theta $
2005
JEE Mains
MCQ
AIEEE 2005
Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$ axis at which the net electric field due to these two point charges is zero is
A.
${L \over 4}$
B.
$2$ $L$
C.
$4$ $L$
D.
$8$ $L$
2005
JEE Mains
MCQ
AIEEE 2005
Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q.$ The potential difference between the centres of the two rings is
A.
${q \over {2\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]$
B.
${{qR} \over {4\pi \,{ \in _0}\,{d^2}}}$
C.
${q \over {4\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]$
D.
zero
2004
JEE Mains
MCQ
AIEEE 2004
A charge particle $'q'$ is shot towards another charged particle $'Q'$ which is fixed, with a speed $'v'$. It approaches $'Q'$ upto a closest distance $r$ and then returns. If $q$ were given a speed of $'2v'$ the closest distances of approaches would be
A.
$r/2$
B.
$2r$
C.
$r$
D.
$r/4$
2004
JEE Mains
MCQ
AIEEE 2004
A charged oil drop is suspended in a uniform field of $3 \times {10^4}$ $v/m$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $ = 9.9 \times {10^{ - 15}}\,\,kg$ and $g = 10\,m/{s^2}$)
A.
$1.6 \times {10^{ - 18}}\,C$
B.
$3.2 \times {10^{ - 18}}\,C$
C.
$3.3 \times {10^{ - 18}}\,C$
D.
$4.8 \times {10^{ - 18}}\,C$
2004
JEE Mains
MCQ
AIEEE 2004
Four charges equal to -$Q$ are placed at the four corners of a square and a charge $q$ is at its center. If the system is in equilibrium the value of $q$ is
A.
$ - {Q \over 2}\left( {1 + 2\sqrt 2 } \right)$
B.
${Q \over 4}\left( {1 + 2\sqrt 2 } \right)$
C.
$ - {Q \over 4}\left( {1 + 2\sqrt 2 } \right)$
D.
${Q \over 2}\left( {1 + 2\sqrt 2 } \right)$
2004
JEE Mains
MCQ
AIEEE 2004
Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that $B$ but uncharged is brought in contact with $B,$ then brought in correct with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is
A.
$F/8$
B.
$3$ $F/4$
C.
$F/4$
D.
$3$ $F/8$
2003
JEE Mains
MCQ
AIEEE 2003
A thin spherical conducting shell of radius $R$ has a charge $q.$ Another charge $Q$ is placed at the center of the shell. The electrostatic potential at a point $P$ a distance ${R \over 2}$ from the center of the shell is
A.
${{2Q} \over {4\pi {\varepsilon _0}R}}$
B.
${{2Q} \over {4\pi {\varepsilon _0}R}} - {{2q} \over {4\pi {\varepsilon _0}R}}$
C.
${{2Q} \over {4\pi {\varepsilon _0}R}} + {q \over {4\pi {\varepsilon _0}R}}$
D.
${{\left( {q + Q} \right)2} \over {4\pi {\varepsilon _0}R}}$
2003
JEE Mains
MCQ
AIEEE 2003
Three charges $ - {q_1}, + {q_2}$ and $ - {q_3}$ are placed as shown in the figure. The $x$-component of the force on $ - {q_1}$ is proportional to
A.
${{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}\cos \theta $
B.
${{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\sin \theta $
C.
${{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\cos \theta $
D.
${{{q_2}} \over {{b^2}}} - {{{q_3}} \over {{a^2}}}sin\theta $
2003
JEE Mains
MCQ
AIEEE 2003
If the electric flux entering and leaving an enclosed surface respectively is ${\phi _1}$ and ${\phi _2},$ the electric charge inside the surface will be
A.
$\left( {{\phi _2} - {\phi _1}} \right){\varepsilon _0}$
B.
$\left( {{\phi _2} + {\phi _1}} \right)/{\varepsilon _0}$
C.
$\left( {{\phi _1} - {\phi _2}} \right)/{\varepsilon _0}$
D.
$\left( {{\phi _1} + {\phi _2}} \right){\varepsilon _0}$
2002
JEE Mains
MCQ
AIEEE 2002
If a charge $q$ is placed at the center of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is
A.
$Q/2$
B.
$ - Q/2$
C.
$Q/4$
D.
$ - Q/4$
2002
JEE Mains
MCQ
AIEEE 2002
A charged particle $q$ is placed at the centre $O$ of cube of length $L(ABCDEFGH).$ Another same charge $q$ is placed at a distance $L$ from $O$. Then the electric flux through $ABCD$ is
A.
$q/4\,\pi \,{ \in _0}L$
B.
zero
C.
$q/2\,\pi \,{ \in _0}L$
D.
$q/3\,\pi \,{ \in _0}L$
2002
JEE Mains
MCQ
AIEEE 2002
On moving a charge of $20$ coulomb by $2$ $cm,$ $2$ $J$ of work is done, then the potential differences between the points is
A.
$0.1$ $V$
B.
$8$ $V$
C.
$2V$
D.
$0.5$ $V.$