Electrostatics: Electric Field Study Notes
1. Electric Field & Intensity
The space around a charge where its influence is felt is the Electric Field.
Intensity ($\vec{E}$): Force per unit test charge.
📝 Doodle: Draw a small sun-like charge with rays going out!
2. Field due to Point Charge
For a charge $Q$ at distance $r$, the field is:
3. Group of Charges (Superposition)
Net field is the Vector Sum of all individual fields.
$\vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + … + \vec{E}_n$
4. Continuous Charge Distribution
When charges are spread over a line, surface, or volume:
- Linear ($\lambda$): $dq = \lambda dl$
- Surface ($\sigma$): $dq = \sigma dS$
- Volume ($\rho$): $dq = \rho dV$
5. Rectangular Components
Resolving $\vec{E}$ into $E_x, E_y, E_z$ components:
$\vec{E} = E_x\hat{i} + E_y\hat{j} + E_z\hat{k}$
Where $E_x = \frac{1}{4\pi\epsilon_0} \frac{qx}{r^3}$ etc. 📐 (Triangle Doodle)
6. Physical Significance
It helps us understand how Forces are transmitted through space even without contact. It defines the electrical environment around a charge.
7. Electric Field Lines
Imaginary smooth curves representing the field direction.
- Start from $(+)$ and end at $(-)$.
- Tangent gives Direction of $\vec{E}$.
- Two lines NEVER intersect. ❌
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JOIN TUTORIAL NOW ⚡Field Intensity on Equatorial Line ⚡
Consider an electric dipole with charges -q and +q separated by 2a. We calculate electric field $E$ at point P on the equatorial line at distance r.
Step 1: Magnitude of fields $E_1$ and $E_2$ are equal:
Step 2: Resultant intensity $E$ is the sum of cosine components:
Substituting $\cos \theta = \frac{a}{(r^2 + a^2)^{1/2}}$:
For a Short Dipole ($r >> a$), the formula becomes:
$E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$
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