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According to the tangent law in magnetism when the magnet is suspended under the combined action of two uniform magnetic field of strengths F and H acting at 90° ,to each other , the magnet comes to rest making an angle x with the direction of H such that F=H tan x.
In the given figure , NS is a bar magnet of length 2l, strength of each pole = M and and dipole moment M= m × 2l .Under the combined action of two mutually perpendicular fields F and H , the magnet comes to rest at an angle x with H.
A couple acts on the magnet due to each magnetic field. In equilibrium the moments of the two couples balance each other.
Draw NA parallel to H and SA parallel to F . Let them meet at A.
Moment of couple due to field H = mH × SA
It is in anticlockwise direction.
Moment of couple due to field F = mF × NA
It is in clockwise direction . In equilibrium the moments of two couples must be equal , that is ,
mH × SA = mF × NA
Or , F= H × (SA/NA) = H tan x
i.e ,. F=H tan x
Which proves the tangent law.
Usually , H is horizontal component of Earth's field and F is is field due to magnetic dipole or current loop.
In the given figure , NS is a bar magnet of length 2l, strength of each pole = M and and dipole moment M= m × 2l .Under the combined action of two mutually perpendicular fields F and H , the magnet comes to rest at an angle x with H.
A couple acts on the magnet due to each magnetic field. In equilibrium the moments of the two couples balance each other.
Draw NA parallel to H and SA parallel to F . Let them meet at A.
Moment of couple due to field H = mH × SA
It is in anticlockwise direction.
Moment of couple due to field F = mF × NA
It is in clockwise direction . In equilibrium the moments of two couples must be equal , that is ,
mH × SA = mF × NA
Or , F= H × (SA/NA) = H tan x
i.e ,. F=H tan x
Which proves the tangent law.
Usually , H is horizontal component of Earth's field and F is is field due to magnetic dipole or current loop.
FAQs on The Tangent Law In Magnetism - Class 12
| 1. What is the Tangent Law in magnetism? |  |
Ans. The Tangent Law in magnetism states that the tangent of the angle between the magnetic field lines and a line drawn perpendicular to the magnetic field at a point on a magnetic field line gives the ratio of magnetic field intensity at that point to the magnetic field intensity at the point where the line intersects the magnetic field again.
| 2. How can the Tangent Law be applied in magnetism? | |
Ans. The Tangent Law can be applied in magnetism to determine the magnetic field intensity at a specific point on a magnetic field line. By measuring the angle between the magnetic field line and a line drawn perpendicular to it, we can calculate the ratio of magnetic field intensities using the tangent function.
| 3. What does the Tangent Law tell us about the strength of a magnetic field? | |
Ans. The Tangent Law provides information about the relative strength of a magnetic field at different points along a magnetic field line. By comparing the tangent values at two different points, we can determine which point has a stronger magnetic field. A larger tangent value indicates a stronger magnetic field intensity.
| 4. Is the Tangent Law applicable to all types of magnets? | |
Ans. Yes, the Tangent Law is applicable to all types of magnets, including permanent magnets and electromagnets. It is a fundamental principle in magnetism that applies to any magnetic field produced by a magnet.
| 5. Can the Tangent Law be used to calculate the magnetic field strength at any point in a magnetic field? | |
Ans. No, the Tangent Law can only be used to calculate the magnetic field strength at points along a magnetic field line. It does not provide information about the magnetic field strength at points not on the field line. Other techniques, such as using the Biot-Savart Law or Ampere's Law, are needed to calculate the magnetic field strength at arbitrary points in a magnetic field.
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