## Electric Charges and Fields

# Electric Field and Electric Field Lines

- Electric field intensity is defined as the force experienced by a unit positive charge placed at a point \tt E = \frac{F}{q}
- If intensity is same at every point both in magnitude and direction it is said to be uniform field.
- If intensity is different at different points then it is Non uniform field.
- Force acting on a charged particle at rest in uniform field is F = Eq.
- Acceleration of a charged particle starting from rest in a uniform field is \tt a = \frac{Eq}{m}
- Final velocity \tt v = \left(\frac{Eq}{m}\right) t & momentum p = (Eq)t
- Displacement \tt S = \frac{1}{2} \left(\frac{Eq}{m}\right)t^{2}
- Kinetic energy oKE = \tt \frac{1}{2} \left(\frac{Eq}{m}\right)^{2} t^{2}
- Null point is the point where the resultant electric field intensity becomes zero.
- Position of null point when charges q
_{1}& q_{2}are separated by a distance d is \tt x = \frac{d}{\sqrt{\frac{q_{2}}{q_{1}}} \pm 1} where {+ like charges and − unlike charges} - Equilibrium condition of charge is EQ = mg

- When charge is suspended from a string

T sin θ = Eq

T cos θ = mg

\tt \tan \theta = \frac{Eq}{mg}

- Tension in the string \tt T = \sqrt{(Eq)^{2} + (mg)^{2}}
- When two identical charged spheres of same mass are suspended by strings of same length
- \tt \frac{F}{l \sin \theta} = \frac{w}{l \cos \theta} = \frac{T}{l} \left\{F = \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{n^{2}}\right\}

- Time period of oscillation of a charged body in electric field \tt T = 2 \pi \sqrt{\frac{l}{\left(g + \frac{Eq}{m}\right)}}

- A line of force is the path along which a unit positive charge accelerates in Electric field.
- Lines of force diverge from positive charge and converge to negative charge.
- The tangent at any point to line of force gives the direction of the field at that point.
- Lines of force never intersect.

### View the Topic in this video From 3:53 To 41:44

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1. Electric field intensity (\overrightarrow{E}): The electric field intensity at any point is defined as the force experienced by a unit positive charge placed at that point.

\overrightarrow{E} = \frac{\overrightarrow{F}}{q_{0}} = \frac{kQ}{r^{2}}

2. Charge may not affect the source charge Q and its electric field is not changed, for electric field intensity

\overrightarrow{E} = \lim_{q_{0} \rightarrow 0} \frac{\overrightarrow{F}}{q_{0}}

3. Electric field intensity and electric potential due to a point charge q, at a distance *t*_{1} + *t*_{2} where *t*_{1} is thickness of medium of dielectric constant *K*_{1} and *t*_{2} is thickness of medium of dielectric constant *K*_{2} are:

E = \frac{1}{4 \pi \varepsilon_{0}}\frac{Q}{\left(t_{1}\sqrt{K_{1}} + t_{2}\sqrt{K_{2}}\right)^{2}}; V = \frac{1}{4 \pi \varepsilon_{0}}\frac{Q}{\left(t_{1}\sqrt{K_{1}} + t_{2}\sqrt{K_{2}}\right)}