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Point charge
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A point charge is an idealized model in physics where a charge is concentrated at a single point with no dimensions. It generates an electric field that radiates uniformly outward, decreasing in strength with the square of the distance.
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Point charge
Storyboard
A point charge is an idealized model in physics where a charge is concentrated at a single point with no dimensions. It generates an electric field that radiates uniformly outward, decreasing in strength with the square of the distance.
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In the case of a spherical Gaussian surface, the electric field ($\vec{E}$) is constant in the direction of the versor normal to the section ($\hat{n}$). Therefore, using the charge ($Q$), the electric field constant ($\epsilon_0$), and the dielectric constant ($\epsilon$), it can be calculated by integrating over the surface where the electric field is constant ($dS$):
with the surface ($S$) for a sphere of radius a distance between charges ($r$):
Thus, the electric field of a point charge ($E_p$) results in:
In the case of a spherical Gaussian surface, the electric field ($\vec{E}$) is constant in the direction of the versor normal to the section ($\hat{n}$). Therefore, using the charge ($Q$), the electric field constant ($\epsilon_0$), and the dielectric constant ($\epsilon$), it can be calculated by integrating over the surface where the electric field is constant ($dS$):
with the surface ($S$) for a sphere of radius a distance between charges ($r$):
Thus, the electric field of a point charge ($E_p$) results in:
The electric potential, point charge ($\varphi_p$) is calculated from the radial integration of the electric field of a point charge ($E_p$) from the radius ($r$) to infinity, which results in
On the other hand, for the charge ($Q$), the dielectric constant ($\epsilon$), and the electric field constant ($\epsilon_0$), the value of the electric field of a point charge ($E_p$) is
This implies that by integrating
$\varphi_p = -\displaystyle\int_{r}^{\infty} du \displaystyle\frac{ Q }{4 \pi \epsilon_0 \epsilon u^2 }= -\displaystyle\frac{ Q }{ 4 \pi \epsilon_0 \epsilon }\displaystyle\frac{1}{ r }$
we obtain
The electric potential, point charge ($\varphi_p$) is calculated from the radial integration of the electric field of a point charge ($E_p$) from the radius ($r$) to infinity, which results in
On the other hand, for the charge ($Q$), the dielectric constant ($\epsilon$), and the electric field constant ($\epsilon_0$), the value of the electric field of a point charge ($E_p$) is
This implies that by integrating
$\varphi_p = -\displaystyle\int_{r}^{\infty} du \displaystyle\frac{ Q }{4 \pi \epsilon_0 \epsilon u^2 }= -\displaystyle\frac{ Q }{ 4 \pi \epsilon_0 \epsilon }\displaystyle\frac{1}{ r }$
we obtain
Examples
In the case of a spherical Gaussian surface, the electric field ($\vec{E}$) is constant in the direction of the versor normal to the section ($\hat{n}$). Therefore, using the charge ($Q$), the electric field constant ($\epsilon_0$), and the dielectric constant ($\epsilon$), it can be calculated by integrating over the surface where the electric field is constant ($dS$):
with the surface ($S$) for a sphere of radius a distance between charges ($r$):
Thus, the electric field of a point charge ($E_p$) results in:
The electric potential, point charge ($\varphi_p$) is calculated from the radial integration of the electric field of a point charge ($E_p$) from the radius ($r$) to infinity, which results in
On the other hand, for the charge ($Q$), the dielectric constant ($\epsilon$), and the electric field constant ($\epsilon_0$), the value of the electric field of a point charge ($E_p$) is
This implies that by integrating
$\varphi_p = -\displaystyle\int_{r}^{\infty} du \displaystyle\frac{ Q }{4 \pi \epsilon_0 \epsilon u^2 }= -\displaystyle\frac{ Q }{ 4 \pi \epsilon_0 \epsilon }\displaystyle\frac{1}{ r }$
we obtain
As illustrated in the following graph:
the field at two points must have the same energy. Therefore, the variables the charge ($Q$), the particle mass ($m$), the speed 1 ($v_1$), the speed 2 ($v_2$), and the electric potential 1 ($\varphi_1$) according to the equation:
and the electric potential 2 ($\varphi_2$), according to the equation:
must satisfy the following relationship:
The electric field of a point charge ($E_p$) is a function of the charge ($Q$), the electric field constant ($\epsilon_0$), the dielectric constant ($\epsilon$), and the distance between charges ($r$) and is calculated as follows:
The electric field of a point charge ($E_p$) is a function of the charge ($Q$), the electric field constant ($\epsilon_0$), the dielectric constant ($\epsilon$), and the distance between charges ($r$) and is calculated as follows:
The electric potential, point charge ($\varphi_p$) is with the charge ($Q$), the distance between charges ($r$), the dielectric constant ($\epsilon$) and the electric field constant ($\epsilon_0$) equal to:
The electric potential, point charge ($\varphi_p$) is with the charge ($Q$), the distance between charges ($r$), the dielectric constant ($\epsilon$) and the electric field constant ($\epsilon_0$) equal to:
Electric potentials, which represent potential energy per unit of charge, influence how the velocity of a particle varies. Consequently, due to the conservation of energy between two points, it follows that in the presence of variables the charge ($q$), the particle mass ($m$), the speed 1 ($v_1$), the speed 2 ($v_2$), the electric potential 1 ($\varphi_1$), and the electric potential 2 ($\varphi_2$), the following relationship must be satisfied:
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