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 q1 & q2 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 t1 + t2 where t1 is thickness of medium of dielectric constant K1 and t2 is thickness of medium of dielectric constant K2 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)}