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Questions and Answers
When dealing with continuous charge distributions, which assumption allows us to simplify calculations?
When dealing with continuous charge distributions, which assumption allows us to simplify calculations?
- The charge is spread continuously across a region. (correct)
- The charge is evenly spaced.
- The charge is concentrated at a single point.
- The charge is quantized in nature.
In the formula $\vec{F} = \frac{q_0}{4\pi\epsilon_0} \int \frac{dq}{r^2}\hat{r}$, what does $dq$ represent?
In the formula $\vec{F} = \frac{q_0}{4\pi\epsilon_0} \int \frac{dq}{r^2}\hat{r}$, what does $dq$ represent?
- The electric field at a point.
- The distance between the charges.
- The total charge of the distribution.
- A differential element of charge in the distribution. (correct)
What is the significance of $\hat{r}$ in the equation $\vec{df}=\frac{1}{4\pi\epsilon_0} \frac{dq}{r^2} \hat{r}$?
What is the significance of $\hat{r}$ in the equation $\vec{df}=\frac{1}{4\pi\epsilon_0} \frac{dq}{r^2} \hat{r}$?
- It is the position vector of $dq$.
- It indicates the direction of the electric field due to $dq$. (correct)
- It represents the magnitude of the electric field.
- It scales the charge element $dq$.
Consider a uniformly charged sphere. How does the electric field at a point outside the sphere compare when calculated using continuous charge distribution versus assuming the entire charge is at the center?
Consider a uniformly charged sphere. How does the electric field at a point outside the sphere compare when calculated using continuous charge distribution versus assuming the entire charge is at the center?
How does the concept of continuous charge distribution relate to the equation $Q = ne$?
How does the concept of continuous charge distribution relate to the equation $Q = ne$?
Flashcards
Continuous Charge Distribution
Continuous Charge Distribution
Charge is spread continuously throughout a region, not as discrete particles.
Elementary Charge (e)
Elementary Charge (e)
The smallest unit of charge that can exist independently.
Force due to Continuous Charge
Force due to Continuous Charge
Force exerted on a test charge due to a continuous charge distribution.
dq (Infinitesimal Charge)
dq (Infinitesimal Charge)
Infinitesimal charge element used in calculating the force due to a continuous charge distribution.
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Permittivity of Free Space ($\epsilon_0$)
Permittivity of Free Space ($\epsilon_0$)
A constant relating electric fields to the charges creating them.
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- Q = ne
Continuous Charge Distribution
- In practice, the magnitude of charges dealt with is much greater than the charge on an electron
- Due to the magnitude difference, the quantum nature of charges can be ignored and it can be imagined that the charge is spread in a region in a continuous manner
- The charge distribution is known as continuous charge distribution
Formula
- F = (q₀ / 4πε₀) ∫(dq / r²) * r̂
df Formula
- df = (1 / 4πε) (dq / r²) * r̂
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