Two uniformly large parallel thin plates having charge densities +σ and -σ are kept in the X-Z plane at a distance 'd' apart. Sketch an equipotential surface due to electric field between the plates. If a particle of mass m and charge '-q' remains stationary between the plates, what is the magnitude and direction of this field?
Two small identical electrical dipoles AB and CD, each of dipole moment 'p' are kept at an angle of 120º as shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field () directed along +X direction,
what will be the magnitude and direction of the torque acting on this?
Here the red dotted lines represent the parallel equipotential surfaces along X-Z plane.
If a charge q has to be held stationary between the two plates, it will have to be balanced by two forces.
Gravitational force: mg, downwards
Electrostatic force = 2qE, acting upwards
This implies that in XZ plane, the upper plate is + charged plate and lower plate is -charged plate.
So, E field lines have to be directed along -y axis.
Resultant dipole moment,
Direction of resultant dipole moment :
That is, 30 degrees with +x axis.
Given applied E is along +x axis,
So torque on resultant dipole will be
τ = pEsin30 = pE /2
Direction will be along -z axis.
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