Answer

Verified

414.3k+ 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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE