Respuesta :
Answer:
The potential difference, ΔV, between two points in the electric field can be described as the potential energy transferred per unit charge, ΔU/q₀ , between the two points
ΔV = ΔU/q₀
Explanation:
The force, F, acting on a test charge, q₀, placed in an electric field E is given as follows;
F = q₀·E
The work the electric field does on the charge, W =dU = F·ds = q₀·E''·dS
[tex]\Delta U = q_0 \times \int\limits^B_A {E \cdot } \, ds[/tex]
The electric potential difference, ΔV, between two points in the electric which is the change in the energy of the system when a test charge is moved between points in the field is goven as follows;
[tex]\Delta V = \dfrac{\Delta U}{q_0} = -\int\limits^B_A {E \cdot } \, ds[/tex]
Therefore, given that, we have;
[tex]\Delta V = \dfrac{\Delta U}{q_0} = \dfrac{-q_o \times \int\limits^B_A {E \cdot } \, ds}{q_0} = \dfrac{F \cdot ds}{q_0} = \dfrac{W}{q_0}[/tex]
Therefore, the potential energy transferred per unit charge, ΔU/q₀ can be described as the potential difference between two points in the electric field, and vice versa.
A force(F), acting on a charged particle, [tex]q_0[/tex], placed in an electric field E is given by the following:
[tex]\to F = q_0 \times E[/tex]
- An effect of an electromagnetic current on a charge
[tex]\to W =dU = F\times ds = q_0 \times E''\times dS\\\\ \to \Delta U= q_0 \times \int^{B}_{A} \ E \cdot ds\\\\[/tex]
- An electric potential differential, [tex]\Delta V[/tex], across two places inside the electric field, that represents the change in energy of a system when a testing charge is moved between points in the field, is calculated as follows.
[tex]\to \Delta V =\frac{\Delta U}{q_0} =-\int^{B}_{A} E \cdot ds\\\\[/tex]
- Therefore, given that, we have;
[tex]\to \Delta V =\frac{\Delta U}{q_0} = \frac{-q_0 \times \int^{B}_{A} E \cdot ds}{q_0} =\frac{F \cdot ds}{q_0}=\frac{W}{q_0}\\\\[/tex]
- As a result, the potential energy transmitted per unit charge, [tex]\frac{\Delta U}{q_0}[/tex], may be represented as the potential difference between two places in the electromagnetic current, and vice versa.
So, the final answer is:
- A potential difference, [tex]\Delta V[/tex], between 2 points in an electric field could be described as the potential power transmitted per unit of charge, [tex]\frac{\Delta U}{q_0}[/tex], between the 2 points.
[tex]\to \Delta V=\frac{\Delta U}{q_0}[/tex]
Learn more about the potential difference:
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