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Point charges, similar to electrons, are among the key construction squares of issue. Additionally, round charge movements (like charge on a metal circle) make external electric fields definitively like a point charge. The electric potential on account of a point charge is, henceforth, a case we need to consider.
We can use math to notice the work expected to move a test charge q from a gigantic distance away to a distance of r from a point charge q. Seeing the relationship among work and conceivable W=-q V, as in the last section, we can secure the going with result.
Electric Potential Due to a Point Charge
A review that the electric potential is depicted as the electric potential energy per unit charge
V = PE/q
The electric potential lets you know how much potential energy alone point charge at a given locale will have. The electric potential at a point is indistinguishable from the electric likely energy (surveyed in joules) of any charged molecule at that area confined by the charge (evaluated in coulombs) of the molecule. Since the charge of the test molecule has been secluded out, the electric potential is a “property” related obviously to the electric field itself and not the test particle. One more method for managing saying this is that since PE is subject to q, the q in the above condition will adjust, so V isn’t reliant upon q.
The potential at boundlessness is picked to be zero. Along these lines, V for a point blame reduces for distance, while E for a point blames decreases for distance squared:
E = F/q
E = kQ/r2
Where k is coulomb force constant,
Q is the charge, and
r is distance from the charge Q where electric field is calculated.
The electric potential is a scalar while the electric field is a vector. Note the harmony between electric potential and gravitational potential – both drop off as a part of distance to the essential power, while both the electric and gravitational fields drop off as a component of distance to the resulting power.
Electric Potential for a multiple charge
Potential of Many Point Charges
By the superposition head, the electric potential emerging from many point charges is
Just:
V=in Kqi / ri
where qi is the charge of the ith charge, and ri is the separation from the charge to some
guide P where we wish to know the absolute electric potential. The benefit of this
computation is that you just need to straightly add the electric potential emerging from each
point charge, rather than adding every vector part independently as on account of the
electric field.
On account of 3 Charges:
If three charges q1, q2, and q3 are arranged at the vertices of a triangle, the expected energy of the framework is,
U =U12 + U23 + U31 = (1/4πε0) × [q1q2/d1 + q2q3/d2 + q3q1/d3]
On account of 4 Charges:
If four charges q1, q2, q3 and q4 are arranged at the sides of a square, the electric likely energy of the framework is,
U = (1/4πε0) × [(q1q2/d) + (q2q3/d) + (q3q4/d) + (q4q1/d) + (q4q2/√2d) + (q3q1/√2d)]
Unique Case:
In the field of a charge Q, assuming a charge q is moved against the electric field from a distance ‘a’ to a distance ‘b’ from Q, the work done is given by,
W = (Vb – Va) × q
= [1/4πεo × (Qq/b)] – [1/4πεo × (Qq/a)]
= Qq/4πεo[1/b – 1/a]
= (Qq/4πεo)[(a-b)/ab]
Conclusion
This article explains electric potential and its calculation for a point charge. V=kQ/r V = k Q / r is the electric potential of a point charge. Electric potential is a scalar, and electric field is a vector. The total electric potential is obtained by adding the voltages as numbers, whereas the total electric field is obtained by adding the individual fields as vectors. A dipole is a pair of opposite charges with equal magnitudes separated by a distance. The electric potential due to a point charge q at a distance of r from that charge is given by, V = (1/4πε0) q/r. Where ε0 is the permittivity of free space.
