# A charge \[q = 10\,{\text{mC}}\] is distributed uniformly over the circumference of a ring of radius \[3\,{\text{m}}\] placed on x-y plane with its centre at origin. Find the electric potential at a point \[P\left( {0,0,4\,{\text{m}}} \right)\]

A. \[18\,{\text{V}}\]

B. \[1.8 \times {10^2}\,{\text{V}}\]

C. \[1.8 \times {10^3}\,{\text{V}}\]

D. \[1.8 \times {10^7}\,{\text{V}}\]

Answer

Verified

289.5k+ views

**Hint:**First of all, we will find the shortest distance between the point and the charge. Then we will apply the formula and substitute the required values and manipulate accordingly to find the electric potential.

**Complete step by step answer:**In the given question, we are supplied with the following data:

The charge present which is uniformly distributed over the circumference of a ring is \[10\,{\text{mC}}\] .

The radius of the ring is \[3\,{\text{m}}\] .

We are asked to find the electric potential at a point \[P\left( {0,0,4\,{\text{m}}} \right)\] .

To proceed the numerical, we will convert the unit of charge to S.I units:

We know,

\[1\,{\text{mC}} = 1 \times {10^{ - 3}}\,{\text{C}}\]

So, we have:

\[10\,{\text{mC}} = 10 \times {10^{ - 3}}\,{\text{C}}\]

Now, we need to find the electric potential due to the given charge, at a point which is at a distance of \[3\,{\text{m}}\] from the charge.

So, we calculate the shortest distance between them by using the Pythagoras theorem, as given below:

\[

r = \sqrt {{3^2} + {4^2}} \\

r = \sqrt {9 + 16} \\

r = \sqrt {25} \\

r = 5\,{\text{m}} \\

\]

Therefore, the shortest distance has come out to be \[5\,{\text{m}}\] .

Now, to find the electric potential we apply the formula, as given below:

\[V = \dfrac{{Kq}}{r}\] …… (1)

Where,

\[V\] indicates electric potential at a point.

\[K\] indicates Coulomb’s constant.

\[q\] indicates point charge.

\[r\] indicates the shortest distance between the circumference and the given point.

Substituting the required values in the equation (1), we get:

\[

V = \dfrac{{Kq}}{r} \\

V = \dfrac{{9 \times {{10}^9} \times 10 \times {{10}^{ - 3}}}}{5} \\

V = \dfrac{{90 \times {{10}^6}}}{5} \\

V = 1.8 \times {10^7}\,{\text{V}} \\

\]

Hence, electric potential at a point \[P\left( {0,0,4\,{\text{m}}} \right)\] is \[1.8 \times {10^7}\,{\text{V}}\] .

**The correct option is D.**

**Additional information:**

An electrical potential is the amount of effort required to transfer a unit of electrical charge from a reference point to a particular point in an electrical field without generating an acceleration (also called the electrical field potential, potential decrease, or electrostatic potential).

**Note:**While solving the numerical, many students tend to make mistake by taking the distance as \[3\,{\text{m}}\] into account, however it is \[5\,{\text{m}}\] , as it is located in space. So, we need to find the shortest distance between the point charge and the point mentioned in the question.

Last updated date: 29th May 2023

•

Total views: 289.5k

•

Views today: 3.46k

Recently Updated Pages

Most eubacterial antibiotics are obtained from A Rhizobium class 12 biology NEET_UG

Salamin bioinsecticides have been extracted from A class 12 biology NEET_UG

Which of the following statements regarding Baculoviruses class 12 biology NEET_UG

Sewage or municipal sewer pipes should not be directly class 12 biology NEET_UG

Sewage purification is performed by A Microbes B Fertilisers class 12 biology NEET_UG

Enzyme immobilisation is Aconversion of an active enzyme class 12 biology NEET_UG

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE