Question
Derive expression for electric field intensity due to a point charge in a material medium.
✓
Answer
i. Consider a point charge q placed at point O in a medium of dielectric constant K as shown in figure
ii. Consider the point P in the electric field of point charge at distance r from q. A test charge q0 placed at the point P will experience a force which is given by the Coulomb’s law,
$\vec{F}=\frac{1}{4 \pi \varepsilon_0 K} \frac{ qq _0}{ r ^2} \hat{ r }$
where $\hat{r}$ is the unit vector in the direction of force i.e., along $O P$.
iii. By the definition of electric field intensity,
$\vec{F}=\frac{F}{ q _0}=\frac{1}{4 \pi \varepsilon_0 K} \frac{ q }{ r ^2} \hat{ r }$
The direction of $\vec{E}$ will be along OP when $q$ is positive and along PO when q is negative.
iv. The magnitude of electric field intensity in a medium is given by, $E=\frac{1}{4 \pi \varepsilon_0 K} \frac{q}{r^2}$
v. For air or vacuum, K = 1 then
$E =\frac{1}{4 \pi \varepsilon_0} \frac{ q }{ r ^2}$
ii. Consider the point P in the electric field of point charge at distance r from q. A test charge q0 placed at the point P will experience a force which is given by the Coulomb’s law,
$\vec{F}=\frac{1}{4 \pi \varepsilon_0 K} \frac{ qq _0}{ r ^2} \hat{ r }$
where $\hat{r}$ is the unit vector in the direction of force i.e., along $O P$.
iii. By the definition of electric field intensity,
$\vec{F}=\frac{F}{ q _0}=\frac{1}{4 \pi \varepsilon_0 K} \frac{ q }{ r ^2} \hat{ r }$
The direction of $\vec{E}$ will be along OP when $q$ is positive and along PO when q is negative.
iv. The magnitude of electric field intensity in a medium is given by, $E=\frac{1}{4 \pi \varepsilon_0 K} \frac{q}{r^2}$
v. For air or vacuum, K = 1 then
$E =\frac{1}{4 \pi \varepsilon_0} \frac{ q }{ r ^2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Two galaxies of masses $9$ billion solar mass and $4$ billion solar mass are $5$ million light years apart. If, the Sun has to cross the line joining them, without being attracted by either of them, through what point it should pass? [Ans: $3$ million light years from the $9$ billion solar mass]
→Derive an expression for critical velocity of a satellite.
Explain the concept of range of the signal.
Two forces, $F_1$ and $F_2,$ each of magnitude $5 N$ are inclined to each other at $60^\circ.$ Find the magnitude and direction of their resultant force.
→Explain ground wave propagation
Derive expression for electric field when an electron of mass $m$ is subjected to an electric field $(E).$
→Describe in detail formation of holes in ii. intrinsic semiconductor.
What are some electrical properties of semiconductors?
Explain any four application of p-n junction diode.
Explain the I-V characteristic of a forward biased junction diode.