Name: Electric Field Produced by a Dipole
Uploaded: 2019-07-19
Duration: 32 min 17 s
Description: What is the electric field of a dipole? Watch the video to understand how the vector addition can be used to determine the electric field of a dipole.

Question

Define capacitance of a capacitor. Derive expression for stored energy between plates of parallel plate capacitor. Show that energy-density between plates of the capacitor can be expressed as

E = \frac{1}{2} ε_{o} E^{2}

, when E= Electric field between plates.

Accepted Answer

The capacity of capacitor: It is defined as the ratio of charge given to plates of the capacitor and the potential difference between two plates of the capacitor.

$C = \frac{Q}{V} = \frac{Q}{V_{1} - V_{2}}$

Expression for energy stored in capacitor: if $q$ is the charge on the plate of capacitor then $q = C V$

Suppose battery supplies an infinitesimally small amount of charge $d q$ capacitor at constant potential $V .$ Then work done

$d W = v d q = \frac{q}{C} d q$

Now, energy stored in charging from $q = 0$ to $q = Q$

$W = \frac{1}{C} \int_{0}^{Q} q d q = \frac{1}{C} {[\frac{q^{2}}{2}]}_{0}^{Q} = \frac{1}{2} \frac{Q^{2}}{C}$

This work done is stored in the form of potential energy

$U = \frac{1}{2} \frac{Q^{2}}{C} = \frac{1}{2} C V^{2}$

Substituting

$C = \frac{Q}{V}; U = \frac{1}{2} Q V$

Energy density: The energy stored in capacitor $U = \frac{1}{2} C V^{2}$ -----(1)

Capacity of capacitor $C = \frac{A ε_{0}}{d}$

Potential $V = E d$

Putting the value of C and V in eq(1)

$U = \frac{1}{2} \frac{A ε_{0}}{d} E^{2} d^{2} = \frac{1}{2} a ε_{0} E^{2} d$

Energy stored in unit volume

$\frac{U}{A d} = \frac{1}{2} \frac{A ε_{0} E^{2} d}{A d}$

The energy stored in unit volume is called Energy density.

$U_{E} = \frac{1}{2} ε_{0} E^{2}$

Embibe Experts Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 1: Bihar Board-2019

Embibe Experts Physics Solutions for Exercise - Embibe Experts Solutions for Chapter: Electrostatic Potential and Capacitance, Exercise 1: Bihar Board-2019

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