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Difficulty: MediumMagnetism and Earth's Magnetic Field

At the Earth's magnetic poles, the horizontal component of the Earth's magnetic field reaches its maximum value while the vertical component is equal to zero.

Answer: Answer

Answer

The statement is false. At the magnetic poles, the angle of dip is 90∘90^\circ, which means the horizontal component of the Earth's magnetic field is zero and the vertical component is at its maximum.
The statement is false because at the Earth's magnetic poles, the angle of inclination (dip) is 90∘90^\circ. Substituting this angle into the component resolution formulas yields Bh=Bcos⁡90∘=0B_h = B \cos 90^\circ = 0 and Bv=Bsin⁡90∘=BB_v = B \sin 90^\circ = B. Therefore, the horizontal component is zero and the vertical component is maximum at the poles.

Step-by-Step Solution

1
Determine the angle of dip (θ\theta) at the Earth's magnetic poles.
The angle of dip at the poles is θ=90∘\theta = 90^\circ.
The Earth's magnetic flux lines enter or leave the surface vertically at the magnetic poles.
2
Calculate the horizontal component (BhB_h) using the magnetic field resolution formula.
Bh=Bcos⁡(90∘)=0B_h = B \cos(90^\circ) = 0.
Since cos⁡(90∘)=0\cos(90^\circ) = 0, there is no horizontal magnetic field component at the poles.
3
Calculate the vertical component (BvB_v) using the magnetic field resolution formula.
Bv=Bsin⁡(90∘)=BB_v = B \sin(90^\circ) = B.
Since sin⁡(90∘)=1\sin(90^\circ) = 1, the vertical component accounts for the entire total magnetic field intensity.
4
Compare the calculated component values against the given statement.
The statement claims BhB_h is maximum and Bv=0B_v = 0, which contradicts the physical reality where Bh=0B_h = 0 and BvB_v is maximum.
Therefore, the statement is evaluated as false.

Key Concept

Earth's Magnetic Field Components at Magnetic Poles
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Topics

Magnetism and Earth's Magnetic Field

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