Question:
Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils if the same current is flown :
Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils if the same current is flown :
Updated On: Jun 7, 2022
- $ 1:\sqrt{2} $
- $ 1:2 $
- 1:02
- $ \sqrt{3}:1 $
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The Correct Option is A
Solution and Explanation
Suppose the magnetic field produced due to each coil is $B$.
The two coils are kept perpendicular hence, the angle between these is $90^{\circ}$ therefore, the resultant magnetic field is given by
$=\sqrt{B^{2}+B^{2}+2 B. B. \cos 90^{\circ}} $
$=\sqrt{2 B^{2}+2 B^{2} \times 0} $
$=\sqrt{2 B^{2}}=B \sqrt{2}$
Hence, the ratio of magnetic field due to one coil and the resultant magnetic field is given by
$=\frac{B}{\sqrt{2 B}}=1: \sqrt{2}$
The two coils are kept perpendicular hence, the angle between these is $90^{\circ}$ therefore, the resultant magnetic field is given by
$=\sqrt{B^{2}+B^{2}+2 B. B. \cos 90^{\circ}} $
$=\sqrt{2 B^{2}+2 B^{2} \times 0} $
$=\sqrt{2 B^{2}}=B \sqrt{2}$
Hence, the ratio of magnetic field due to one coil and the resultant magnetic field is given by
$=\frac{B}{\sqrt{2 B}}=1: \sqrt{2}$
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
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- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
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- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.