At the equator, the earth's field is essentially horizontal;...

At the equator, the earth's field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth's field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatch lings from a beach where the magnetic field strength is $50 \mu \mathrm{T}$ and the dip angle is $56^{\circ} .$ You then put the turtles in a 1.2 -m-diameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 100 -turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth. What current should you pass through the coil, and in what direction, to produce a net field in the center of the tank that has a dip angle of $62^{\circ} ?$

Key Concepts

Magnetic Field Components

A magnetic field can be decomposed into horizontal and vertical components. Understanding these components is crucial because any net magnetic field is the vector sum of its parts, which is key when manipulating fields in experimental setups.

Magnetic Dip Angle

The dip angle is the angle between the Earth's magnetic field and the horizontal plane. It indicates how much the field deviates from being horizontal, varying with latitude. This concept is central to understanding phenomena influenced by geomagnetic variations.

Magnetic Field Superposition

The principle of superposition states that multiple magnetic fields can be vectorially added to produce a resultant field. This concept is fundamental when using additional magnetic fields, such as those generated by coils, to adjust the net field in an experiment.

Magnetic Field Generated by a Coil

Electromagnetic coils produce magnetic fields that can be varied by changing the current passing through them. The calculation of the resultant field created by a coil is essential in experimental designs where the external field must be precisely controlled or modified.

Transcript

00:02 Hi, in the given problem here, this is the tank in which there is a coil.

00:21 The coil is having the number of turns given as n is equal to 100.

00:39 Diameter of the circular tank is given as 1 .2 meter so its radius r will be half of the diameter means it's 0 .6 meter the magnetic field earth's magnetic field here is b is equal to 50 microtesla at an angle of dip equals to 56 degree and here the angle of dip means if you consider it to be here, this is the earth's magnetic field.

01:29 Then the angle of dip means the angle made by earth's magnetic field with the horizontal in downward direction.

01:38 Delta is angle of dip.

01:40 So there will be two components of earth's magnetic field.

01:45 Horizontal component bh and vertical component.

01:51 Meant bv.

01:55 Now if we pass a current i through the coil, suppose the current passing through the coil is i due to which as here it is given that the angle of dip should be increased to 62 degree and the horizontal component of earth's magnetic field will remain same as bh, means which was given as b, cos, delta.

02:46 So in order to increase the angle of dip, the total vertical component should be increased.

02:55 Net vertical component of magnetic field should be increased to bv dash, which will be equal to the original vertical component plus the magnetic field produced by the coil.

03:18 So it is bv plus b coil using the expression for angle of dip which is given in terms of tangent...

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