Answer

Verified

335.4k+ views

**Hint:**From the given data, we have to find out the magnitude of magnetic field at the common center coil, for this calculation they have given radius and current and number of turns of a coil. For this calculation we are using the magnetic field equation.

**Complete step by step answer:**

A straight current-carrying conductor has a magnetic field in the shape of concentric circles around it. The magnetic field of a straight current-carrying conductor can be visualized by magnetic field lines. The direction of a magnetic field produced due to a current-carrying conductor relies upon the same direction in which the current is flowing.Here,

${r_1} = 5\,cm \\

\Rightarrow {r_2} = 10\,cm \\

\Rightarrow {n_1} = 50 \\

\Rightarrow {n_2} = 100 \\

\Rightarrow i = 2\,A \\ $

When the current coils in the same direction, then from magnetic field,

$B = {B_1} + {B_2} $

magnetic field formula,

${B_1} = \dfrac{{{\mu _ \circ }i{n_1}}}{{2{r_1}}} \\

\Rightarrow {B_2} = \dfrac{{{\mu _ \circ }i{n_2}}}{{2{r_2}}} \\$

Substituting the ${B_1}$and ${B_2}$in the magnetic field, then

$B = \dfrac{{{\mu _ \circ }i{n_1}}}{{2{r_1}}} + \dfrac{{{\mu _ \circ }i{n_2}}}{{2{r_2}}} \to (1)$

Here we know ${\mu _ \circ } = 4\pi \times {10^{ - 7}}$

By adding all the value in equation (1),

$B = \dfrac{{4\pi \times {{10}^{ - 7}} \times 50 \times 2}}{{2 \times 0.05}} + \dfrac{{4\pi \times {{10}^{ - 7}} \times 100 \times 2}}{{2 \times 0.1}}$

Calculating the above values we get the value of B,

$B = 8\pi \times {10^{ - 6}}$

Now we clear that, current in the coils is in the same sense.

Lets calculate the magnetic field in opposite direction

$B = {B_1} - {B_2}$

By adding the same values in opposite direction, we get the value of B

$B = \dfrac{{4\pi \times {{10}^{ - 7}} \times 50 \times 2}}{{2 \times 0.05}} - \dfrac{{4\pi \times {{10}^{ - 7}} \times 100 \times 2}}{{2 \times 0.1}}$

Calculating the above value , $B = 0$. We have proven that the current in the coils are in the opposite sense. Magnitude of the magnetic field at the common center point is proven in the same sense and opposite sense.

**Hence, both options A and C are correct.**

**Note:**Circular coils are in the same sense or in opposite sense we have to prove in two forms. Magnitude of magnetic field ranges from approximately 25 to 65 microtales. Direction of magnetic field defined by right hand rule.magnetic field is which repels the magnet to each other.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Assertion The resistivity of a semiconductor increases class 13 physics CBSE

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The branch of science which deals with nature and natural class 10 physics CBSE

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

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

Give 10 examples for herbs , shrubs , climbers , creepers

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

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

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

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

What organs are located on the left side of your body class 11 biology CBSE