Answer
Verified
380.7k+ views
Hint: By knowing the values of permeability of the material of the soft iron core, number of turns, radius and current passing through the coil we can calculate the magnetic field. So to calculate the magnetic field first we have to calculate the permeability of the soft iron core which is the product of relative permeability, permeability of the material and permeability of free space. Thus substituting these values we will get the magnetic field of toroidal solenoid.
Magnetic field of toroidal solenoid is given by,
\[B=\mu nI\]
Where,
\[n=\dfrac{N}{2\pi r}\]
B is the magnetic field
N is the number of turns
r is the radius
Complete step-by-step solution:
Magnetic field of toroidal solenoid is given by,
\[B=\mu nI\]
Where,
\[n=\dfrac{N}{2\pi r}\]
B is the magnetic field
N is the number of turns
r is the radius
Give that N=3000
r=10cm
I=1.0A
\[{{\mu }_{r}}=2000\]
First we have to calculate n.
\[n=\dfrac{N}{2\pi r}\]
\[n=\dfrac{3000}{2\pi \times 10\times {{10}^{-2}}}\]
Then we can calculate magnetic field using the equation,
\[B=\mu nI\]
Where,
\[\mu ={{\mu }_{r}}{{\mu }_{0}}\]
Thus B becomes,
\[B={{\mu }_{r}}{{\mu }_{0}}nI\]
Then by substituting the values we get,
\[B=2000\times 4\pi \times {{10}^{-7}}\times \dfrac{3000}{2\pi \times 10\times {{10}^{-2}}}\times 1\]
B=12T
Therefore option (2) is correct.
Note: The value of magnetic field B differs with the space. That is, the field inside and outside the toroidal is zero. For a toroid with closely bounded turns, the magnetic field has a constant magnitude. Using the right hand thumb rule we can determine the direction of the magnetic field.
Magnetic field of toroidal solenoid is given by,
\[B=\mu nI\]
Where,
\[n=\dfrac{N}{2\pi r}\]
B is the magnetic field
N is the number of turns
r is the radius
Complete step-by-step solution:
Magnetic field of toroidal solenoid is given by,
\[B=\mu nI\]
Where,
\[n=\dfrac{N}{2\pi r}\]
B is the magnetic field
N is the number of turns
r is the radius
Give that N=3000
r=10cm
I=1.0A
\[{{\mu }_{r}}=2000\]
First we have to calculate n.
\[n=\dfrac{N}{2\pi r}\]
\[n=\dfrac{3000}{2\pi \times 10\times {{10}^{-2}}}\]
Then we can calculate magnetic field using the equation,
\[B=\mu nI\]
Where,
\[\mu ={{\mu }_{r}}{{\mu }_{0}}\]
Thus B becomes,
\[B={{\mu }_{r}}{{\mu }_{0}}nI\]
Then by substituting the values we get,
\[B=2000\times 4\pi \times {{10}^{-7}}\times \dfrac{3000}{2\pi \times 10\times {{10}^{-2}}}\times 1\]
B=12T
Therefore option (2) is correct.
Note: The value of magnetic field B differs with the space. That is, the field inside and outside the toroidal is zero. For a toroid with closely bounded turns, the magnetic field has a constant magnitude. Using the right hand thumb rule we can determine the direction of the magnetic field.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Draw a labelled sketch of the human eye class 12 physics CBSE