Earth's magnetic field

Question

The angle of dip is the angle between earth's horizontal magnetic field and magnetic field produce by coil .

But I could not understand when current is reversed the angle of dip changes but magnitude of magnetic field is same .

Comments

Angle of dip is the angle between the horizontal and the resultant magnetic field. The resultant is the vector sum of the magnetic fields from the Earth and the coil.

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Let $B_v$ and $B_h$ be vertical and horizontal component of magnetic field. K be magnetic field by coil.
Then $B_v/(B_h +k) = tan(30°)$
And $B_v/(B_h-k) = tan(60°)$ .
Now what to do .

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You are given $B_h$. The 2 unknowns are $B_v$ and $K$. Eliminate $B_v$ to find $K$. Then relate that to the current in the coil.

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Here is k equals to $\mu ni$ where n is number of turns . Then what is the use of radius given .

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That is the field on the axis of a very long *solenoid*. The formula for planar *coil* is different and depend on radius.

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You mean B=$\mu _0 ni/2R$

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That is correct. (Note that here n=number of turns, whereas for the solenoid n=number of turns per metre.)

Answer 1

The angle of dip is the angle between the horizontal and the vector sum of the magnetic fields from the Earth and the coil. Reversing the current in the coil reverses the field from the coil and changes the vector sum. You will need to draw vector diagrams.

Comments

I think we cannot draw a vector diagram for it . As I could not understand how it is possible.