1 Marks Question

Question 11 Mark

Two charged particles having charge 2.0 × 10^-8C each are joined by an insulating string of length 1m and the system is kept on a smooth horizontal table. Find the tension in the string.

Answer

Force exerted $=\frac{\text{kq}_1^2}{\text{r}^2}$
$=\frac{9\times10^9\times2\times2\times10^{-16}}{1^2}$
$=3.6\times10^{-6}$ Is the force exerted on the string.

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Question 21 Mark

NaCl molecule is bound due to the electric force between the sodium and the chlorine ions when one electron. of sodium is transferred to chlorine. Taking the separation between the ions to be 2.75 × 10cm, find the force of attraction between them· State the assumptions (if any) that you have made.

Answer

$\text{F}=\frac{\text{kq}_1\text{q}_2}{\text{r}^2}$
$=\frac{9\times10^9\times1.6\times1.6\times10^{-19}\times10^{-19}}{(2.75\times10^{-10})^2}$
$=\frac{23.04\times10^{-29}}{7.56\times10^{-20}}$
$=3.04\times10^{-9}$

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Question 31 Mark

A sample of HCI gas is placed in an electric field of 2.5 × 10⁴NC^-1. The dipole moment of each HCI molecule is 3.4 × 10^-30Cm. Find the maximum torque that can act on a molecule.

Answer

$\text{E}=2.5\times104$
$\text{P}=3.4\times10^{-30}$
$ \text{T}=\text{PE}\sin\theta$
$=\text{P}\times\text{E}\times1$
$=3.4\times10^{-30}\times2.5\times10^4$
$=8.5\times10^{-26}\text{Nm}$

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Question 41 Mark

Two charged particles are placed at a distance 1.0cm apart. What is the minimum possible magnitude of the electric force acting on each charge?

Answer

Minimum charge of a body is the charge of an electron,
$\Rightarrow\text{q}=1.6\times10^{-19}\text{C}$
Given,
Separation between the charges, r = 1cm = 10^-2cm
By Coulomb's Law, force,
$\text{F}=\frac{1}{4\pi\in_0}\frac{\text{q}_1\text{q}_2}{\text{r}^2}$
$=\frac{9\times10^9\times1.6\times1.6\times10^{-19}\times10^{-19}}{10^{-2}\times10^{-2}}$
$=23.04\times10^{-38+9+2+2}$
$=23.04\times10^{-25}$
$=2.3\times10^{-24}$

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Question 51 Mark

Find the dimensional formula of $\in_0.$

Answer

By Coulomb's Law,
$\text{F}=\frac{1}{4\pi\in_0}\frac{\text{q}_1\text{q}_2}{\text{r}^2}$
$\Rightarrow\in_0=\frac{1}{4\pi\text{F}}\frac{\text{q}_1\text{q}_2}{\text{r}^2}$
Using $[\text{F}]=\big[\text{MLT}^{-2}\big]$
$[\text{r}]=\big[\text{M}^0\text{L}^1\text{T}^0\big]$
$[\text{q}]=\big[\text{M}^2\text{L}^0\text{T}^1\text{A}^1\big],$ we get
$[\in_0]=\big[\text{M}^{-1}\text{L}^{-3}\text{T}^4\text{A}^2\big]$

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