# A coil carrying current 1 has radius $r$ and number of units $n$. It is rewound so that the radius of the new coil is $\dfrac{r}{4}$ and it carries current $1$. The ratio of magnetic moment of new coil to that of original coil is

A. $1$

B. $\dfrac{1}{2}$

C. $\dfrac{1}{4}$

D. $\dfrac{1}{8}$

Answer

Verified

281.1k+ views

**Hint:**Coil carrying current radius and number of turns is given and new coil turns radius is given, measure the ratio of magnetic moment.he magnetic moment is a vector quantity. The objects have a tendency to place themselves in such a way that the magnetic moment vector becomes parallel to the magnetic field lines. The direction of the magnetic moment points from the south to the north pole of a magnet.

**Complete step by step answer:**

Initially radius of the coil is $r$ and number of turns of the coil is $n$ respectively,

The initial length of the wire is $L=n\left( {2\pi r} \right)$

Area of the coil is, A=$\pi {r^2}$

From the initial magnetic moment, $\mu = nlA$

Already $A$ value is the area of the coil, then

$\mu = nl\pi {r^2} \to \left( 1 \right)$

Now the same wire is wound to the coil of radius, ${r_1} = \dfrac{r}{4}$

Assuming the number of turns of the coil is, ${n_1}$

The length of the wire is, ${L_1} = {n_1}\left( {2\pi {r_1}} \right)$

Substituting the value of ${r_1}$, then

${L_1} = \dfrac{{2\pi {n_1}r}}{4}$

Suppose ${L_1} = L$ then,

$2\pi rn = \dfrac{{2\pi r{n_1}}}{4} \\

\Rightarrow {n_1} = 4n \\ $

Now area of new coil is

${A_1} = \pi {\left( {{r_1}} \right)^2} \\

\Rightarrow {A_1} = \dfrac{{\pi {r^2}}}{{16}} \\ $

Let us calculate the magnetic moment of the new coil then we get,

${\mu _1} = {n_1}l{A_1}$

We already calculated all the values in left hand side, by substituting those values in the above equation we get,

${\mu _1} = 4nl \times \dfrac{{\pi {r^2}}}{{16}} \\

\Rightarrow {\mu _1} = \dfrac{{nl\pi {r^2}}}{4} \\ $

Therefore,

${\mu _1} = \dfrac{\mu }{4} \\

\therefore \dfrac{{{\mu _1}}}{\mu } = \dfrac{1}{4} \\ $

**Hence the ratio of magnetic moment of the new coil to that of the original coil is, $\dfrac{1}{4}$ and the correct option is C.**

**Note:**Current carrying coil and its radius and number of turns are different from the number of turns of the coil and radius of the coil that carries current of the new coil. Simple defined as, the ratio of magnetic moment of new coil to the magnetic moment of that original coil, which carries different current in both the coils.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Trending doubts

Which country launched the first satellite in space class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

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

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

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