Experiment 17: Earth's Magnetic Field

Experiment 17: Earth’s Magnetic Field

Figure 17.1: Earth’s Magnetic Field - Note that each of the 3 elements of the circuit are connected in series. Note the large power supply: large power supply large current. Use the 20A jack and scale of the ammeter. →

Figure 17.2: Earth’s B-Field Schematic

1 2 Experiment 17: Earth’s Magnetic Field

EQUIPMENT Tangent Galvanometer Ammeter (20A jack, 20A DCA) Dip Needle Large Power Supply (2) 12” Wire Leads (2) 36” Wire Leads Experiment 17: Earth’s Magnetic Field 3

Advance Reading

Text: Magneticﬁeld, vectors, right-hand rule for a wire loop, resistivity.

Objective

The objective of this lab is to measure the magnitude of Earth’s magneticﬁeld in the lab.

Theory

The magneticfield of Earth resembles thefield of a bar Figure 17.3 magnet. All magneticfield lines form a closed loop: a field line originates at the north pole of a magnet, en- The direction of the magneticfield of a current car- ters the south pole, then moves through the magnet it- rying wire is given by the right-hand rule. When the self back to the north pole. Although we usually think thumb of the right hand points in the direction of the of thisfield as two-dimensional (north, south, east, current (positive current; conventional current), the west), remember that it is, in fact, a three-dimensional fingers will curl around the wire in the direction of the vectorfield. magneticfield. Refer to Fig. 17.3. The horizontal component of the magneticfield of Earth is typically measured using a compass. The needle of a compass is a small magnet, which aligns with an external magneticfield. Recall that opposite poles attract, and like poles repel. Thus, the north pole of the compass needle points to the south magnetic pole of Earth, which is sometimes close to the geographic north pole.

We will measure the horizontal component of Earth’s magneticfield, B� e, then use this information to determine the magnitude of the total magneticfield of Earth, B� t. Determining the magnitude of an unknown magnetic field can be accomplished by creating an additional, known magneticfield, then analyzing the netfield. The magneticfields will add (vector math) to a net magneticfield (resultant vector).

B� net = B� known + B� unknown (17.1) Figure 17.4 The known magneticfield, B� galv, will be produced by use of a tangent galvanometer. A tangent galvanome- The coil of the tangent galvanometer isfirst aligned ter is constructed of wire loops with currentflowing with the direction of an unknownfield,B e, or north. through the loops. The current produces a magnetic The compass inside the tangent galvanometer allows field. The magnitude of this magneticfield depends accurate alignment. Once current beginsflowing, the on the current, the number of loops, and the radius of two magneticfields will add (vector addition) to yield each loop: a resultant magneticfield. The compass needle then µ0IN rotates to align with the netfield. The deflection angle Bgalv = (17.2) 2r α is the number of degrees the compass needle moves. α is measured, andB e is calculated from: whereµ = 4π 10 −7 Tm/A is the permeability con- 0 × stant,I is the current,N is the number of loops, and Bgalv r is the radius of the loop. = tanα (17.3) Be 4 Experiment 17: Earth’s Magnetic Field

A typical compass is constrained to 2 dimensions and rotates to point to Earth’s magnetic south pole, which is (approximately) geographic north. Earth’s magnetic ﬁeld, however, is a 3 dimensional phenomenon. It has components that point into and out of the earth, not just along the surface. We need to measure at our location the direction of the total magneticﬁeld of Earth (the angleθ).

To determineﬁeld declination,θ, we will use a dip needle. A dip needle (Fig. 17.5 and Fig. 17.6) is a compass that rotates. It measures both horizontal and vertical angles.

First, arrange the dip needle in a horizontal position, compass needle and bracket aligned, pointing north (normal compass). Refer to Fig. 17.5, below, for clari- ﬁcation. The needle should align with 270◦.

Figure 17.6: Dip Needle: Vertical Orientation

Figure 17.5: Dip Needle: Horizontal Orientation

Figure 17.7 Now rotate the compass 90◦ (Fig. 17.6) to a vertical position. The needle rotates to a new angle; the dif- ference between the initial angle and thefinal angle is the angleθ. By determining the magnitude of the horizontal component of Earth’s magneticfield,B e, usingα, and mea- From Fig. 17.6, we see that the dip needle points in suring the direction of Earth’s total magneticfield,B t, the direction of Earth’s total magneticfield at our lo- usingθ, the magnitude ofB t can be determined. (Re- cation. fer to Fig. 17.7.) Prelab 17: Earth’s Magnetic Field 5

Name:

µ0iN 1. What physical phenomenon does the relationshipB galv = 2r describe? (10 pts)

2. Explain the right-hand rule for current. (10 pts)

3. Consider Fig. 17.4. Determine the following in terms ofB’s (B e,B galv, andB net). (10 pts)

sinθ=

cosθ=

tanθ=

4. Consider Fig. 17.7. Determine the following in terms ofB’s (B e,B z, andB t). (10 pts)

sinα=

cosα=

tanα=

6 5. GivenB of 45 10 − T and a dip angle of 55◦, calculateB . See Fig. 17.7. (30 pts) e × z 6 Prelab 17: Earth’s Magnetic Field

6. Consider the top-view diagram of the tangent galvanometer, Fig. 17.11. Given the galvanometer’s alignment with North, as shown, indicate the direction that currentﬂows through the top of the wire loops. (30 pts)

Figure 17.8: Top View - Wire loops encircle compass. Figure 17.9: Side View - Compass located inside wire loops.

Figure 17.10: Tangent Galvanometer Figure 17.11: Compass Needle 7

Name: Section: Date:

Worksheet - Exp 18: Earth’s Magnetic Field

Objective: Measure the magnitude and direction of the Earth’s magneticﬁeld at this location.

Theory: The magneticfield of Earth resembles the field of a bar magnet. All magneticfield lines form a closed loop: afield line originates at the north pole of a magnet, enters the south pole, then moves through the magnet itself back to the north pole. Although we usually think of thisfield as two-dimensional (north, south, east, west), remember that it is, in fact, a three- dimensional vectorfield.

We will measure the horizontal component of Earth’s magneticﬁeld, B� e, then use this information to determine the magnitude of the total magneticﬁeld of Earth, B� t.

Procedure: Part 1: Horizontal Component

1. Connect the galvanometer (N=5), ammeter (20A DCA), and power supply in series 2. Align the galvanometer such that it creates a magneticfield perpendicular to that of Earth’sfield (the compass needle should be parallel to the wire loop). Do not move the galvanometer while taking data. 3. Turn on the power supply toflow current through the galvanometer. Adjust the current until the compass needle on the galvanometer moves by 30◦, 40◦, and 50◦, record the current required for each angular position in the data table provided. 4. Repeat this process forN = 10 andN = 15 (a total of nine trials). What happens to the current required as N increases? Is this a linear relationship? (8 pts) 8

5. CalculateB e for each of the nine trials. The galvanometer generates a magnetic ﬁeld whose strength depends on current, number of loops, and loop radius as follows:B galv =µ 0IN/2r. The diameter of the coils is approximately 20 cm. 7 [µ = 4π 10 − Tm/A] 0 ×

α = 30◦ α = 40◦ α = 50◦ I: I: I: N = 5

Be: Be: Be:

I: I: I: N = 10

Be: Be: Be:

I: I: I: N = 15

Be: Be: Be:

(54 pts)

6. Find the average value ofB e from your nine trials. (4 pts) AverageB e =

7. Beatrice aligned her galvanometer 90◦ off, so that itsfield was in line with (or against) Earth’s ownfield. As she increased current, the needle remained stationary until it suddenly changed direction at one amount of current. How did the needle behave at this particular current? What can Beatrice conclude about the strength ofB galv at the instant when the needle moves? Draw a sketch of this setup. (14 pts) 9

Part 2: Field Inclination 8. magnetic inclination is the angle made with the horizontal by the Earth’s magneticﬁeld lines. In Oxford MS, the angle of magnetic inclination is approximately 63◦.

9. Use this inclination to calculate the magnitude of the total magneticﬁeld of the Earth in the lab. (4 pts)

Bt =

10. Compare your measuredB t from this experiment to a sample value of 43µT, the magnitude of the magneticﬁeld in Tucson, Arizona. (6 pts)

11. Tucson is approximately two degrees (latitude) south of this lab. Would the inclination of Earth’s magneticﬁeld be greater or lesser than it is here? How do you know? (8 pts)