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The distance between electric charges QC and 9QC is 4m. What is electric potential at a point of the line joining them where the electric field is zero?
(A) 4 kQ v
(B) 10 kQ v
(C) 2 kQ v
(D) 2.5 kQ v

Last updated date: 17th Apr 2024
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Hint: We know that the electric potential, or voltage, is the difference in potential energy per unit charge between two locations in an electric field. When we talked about electric fields, we chose a location and then asked what the electric force would do to an imaginary positively charged particle if we put one there. Note that the electrical potential energy is positive if the two charges are of the same type, either positive or negative, and negative if the two charges are of opposite types.

Complete step-by step answer:
We know that Electric field and electric potential due to charge Q at a distance r is given by $\dfrac{KQ}{{{r}^{2}}}\,and\,\dfrac{KQ}{r}$respectively.
Let us consider that the point (say P) where electric field is zero is x distance apart from the charge QC and (4-x) distance apart from charge 9QC as shown in figure.

Since, the direction of electric field is opposite, their magnitude must be equal in order to get zero electric field.
So, $\dfrac{KQ}{{{x}^{2}}}\,and\,\dfrac{9KQ}{{{(4-x)}^{2}}}$
$\Rightarrow \dfrac{1}{{{x}^{2}}}=\,\dfrac{9}{{{(4-x)}^{2}}}$
$\Rightarrow \dfrac{1}{x}=\,\dfrac{9}{(4-x)}\,\,\Rightarrow x=1m.$
Now, Electric potential at point P = Potential due charge QC + Potential due charge 9QC
$\Rightarrow \dfrac{KQ}{1}+\dfrac{9KW}{3}=4KQv$

Hence, the correct answer is Option A.

Note: We know that electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge. Electric fields originate from electric charges, or from time-varying magnetic fields. The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point.
It should also be known to us that the space around an electric charge in which its influence can be felt is known as the electric field. The electric field Intensity at a point is the force experienced by a unit positive charge placed at that point. Electric Field Intensity is a vector quantity. The electric field lines flow from positive to negative charges. Such sources are well suited for surface applications such as wound healing, corneal repair or even brain and spinal stimulation with closely-separated, inserted electrodes.