The field strength of any point in the point charge system is equal to the vector sum of the field strength generated at the point when each point charge exists alone
Point chargeThe field strength at any point in the system is equal to that generated at that point when the charges at each point exist alonefield strengthThe vector sum of, which is the principle of field strength superposition.
If several point charges exist at the same time, the electric fields generated by them will overlap each other to form a combined electric field. At this time, the field strength of a point is equal to the vector sum of the field strength generated at that point when each charge exists alone.The principle of field strength superposition is actually the principle of force superposition.[1]
The derivation process is as follows:
If the charged body consists of n point charges, as shown in Figure 1
Figure 1
According to the principle of electric power superposition:
Defined by field strength:
After sorting out:
or
If the charged body can be regarded as a continuous distribution of charges, as shown in Figure 2
Figure 2
The charged body is regarded as composed of many charge elements, and then the principle of superposition of field strength is used.
features
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Since the field strength is a vector, it is necessary to find the vector sum of the electric field force on each charge at a certain pointParallelogram rule；
The electric field generated by each charge is independent and does not affect each other;
Using the superposition principle of electric field, the field strength of any charged body at any point can be calculated theoretically.
Formula representation
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The superposition of field strength is not only true for the point charge system, but also true for the electric field generated by any point system.If the field strength distribution of charged body with continuous charge distribution is required, we can regard the charge carried by the charged body as a collection of many tiny charge elements dq, and each charge element dq is treated as a point charge.The electric field strength is the force applied to the unit positive charge:
Electric field intensity of point charge:
Dq The electric field intensity dE generated at a point in the field is
Where, r is the size of the radial vector from dQ to the point, and e is the unit vector.According to the principle of field strength superposition, the combined field strength generated by all charge elements at the point is the vector superposition of the field strength generated by each charge element at the point, that is
It must be pointed out that vector sum and vector integral are taken in the formula, which usually need to be converted into scalar sum or scalar integral for solution.[2]
