Answer

Verified

21.3k+ views

**Hint:**In the question, it’s given that the coin is floating. The coin will float only when the net force is zero or the forces are balanced i.e. the force due to the electric field is equal to the weight of the electron. From this, we can easily calculate the charge required to balance the electron and from that, we can calculate the amount of electron which will be removed.

**Formulae used:**

${N_e} = \dfrac{q}{{{C_e}}}$

Here ${N_e}$ is the number of electrons, $q$ is the total charge and ${C_e}$ is the charge on one electron.

**Complete step by step answer:**

In the question, a coin of mass $1.6g$ is given. It is said that it is floating in the electric field of $109N{C^{ - 1}}$.

Let us draw the free body diagram of the coin.

For the coin to float it should be in a balanced condition. The upward force acting on the coin should be equal to the downward force acting on the body. Hence

$ \Rightarrow qE = mg$

Where $q$ is the net charge on the coin, $E$ is the electric field acting on the body, $m$ is the mass of the coin and $g$ is the acceleration due to gravity.

Let this be equation 1.

It’s given that,

$m = 1.6g = 1.6 \times {10^{ - 3}}kg$

$E = {10^9}N{C^{ - 1}}$

$g = 9.8m{s^{ - 2}}$

Putting the values of $m$, $E$ and $g$ in the equation 1, we get,

$ \Rightarrow q \times 109 = 1.6 \times {10^{ - 3}} \times 9.8$

$ \therefore q = \dfrac{{1.6 \times {{10}^{ - 3}} \times 9.8}}{{{{10}^9}}}$

We know that the charge on one electron is $1.6 \times {10^{ - 19}}C$.

The number of electrons that is required to be removed,

$ \Rightarrow {N_e} = \dfrac{q}{{{C_e}}}$

Here ${N_e}$ is the number of electrons, $q$ is the total charge and ${C_e}$ is the charge on one electron.

$ \Rightarrow {N_e} = \dfrac{q}{{{C_e}}}$

$ \therefore {N_e} = \dfrac{{\dfrac{{1.6 \times {{10}^{ - 3}} \times 9.8}}{{{{10}^9}}}}}{{1.6 \times {{10}^{ - 19}}C}} = 9.8 \times {10^7}$

**So option (A) is the correct answer.**

**Note:**Any charge when placed in an external electric field will experience an electric force. In this case the force experienced by all the electrons in the coin should balance the weight of the coin. We will not consider the electric force acting on the protons because this electric force acting on them is negligible as compared to the intranuclear forces inside the nucleus of the atoms. So, only the force on the electrons is considered.

Recently Updated Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

IfFxdfrac1x2intlimits4xleft 4t22Ft rightdt then F4-class-12-maths-JEE_Main

A rod of certain length is acted by two equal forces class 11 physics JEE_Main

Sodium chloride is purified by passing hydrogen chloride class 11 chemistry JEE_Main

Other Pages

Electric field due to uniformly charged sphere class 12 physics JEE_Main

If the magnetizing field on a ferromagnetic material class 12 physics JEE_Main

An object of 5 cm height is placed at 20 cm in front class 12 physics JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

A household uses the following electric appliances class 12 physics JEE_Main

Define 1 Ohm resistance A student has a resistance class 12 physics JEE_Main