1
AIEEE 2007
+4
-1
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
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
2
AIEEE 2007
+4
-1
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
3
AIEEE 2006
+4
-1
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
4
AIEEE 2006
+4
-1
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
$$1:4$$
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