Rl series circuit calculator

Magnetic Fields – Tangent Galvanometer
Introduction and Theory:

Just like an electric field exists around electric charges, there is a magnetic field surrounding a permanent magnet and around moving electric charges. Since electric current is a flow of charge, there is a magnetic field around any current carrying wire. This magnetic field can be detected by observing the behavior of a compass needle in the presence of current carrying elements. Like an electric field, the magnetic field also is a vector quantity and has both a magnitude and a direction. The direction of a magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point.

The magnetic field of the earth is thought to be caused by convection currents in the outer core of the earth working in concert with the rotation of the earth. The field has a shape very similar to the field produced by a bar magnet. Incidentally, the north magnetic pole of the earth does not coincide with the north geographic pole. In fact, the north magnetic pole is located close to the Earth's South Pole (in Antarctica), while the south magnetic pole is located close to the Earth's North Pole (in Canada).

For a loop of wire consisting of N turns wound close together to form a flat coil with a single radius R, the magnetic field resembles the pattern of a short bar magnet, and its magnitude at the center of the coil according the Biot-Savart law is

(1)

where is the permeability of free space (4π × 10-7 T·m/A) and I is the current in the coil. If the current is expressed in amperes (A), and the radius in meters (m), the unit of magnetic field strength is Tesla (T). Note that this field vector is parallel to the axis of the coil. In many situations the magnetic field has a value considerably less than one Tesla. For example, the strength of the magnetic field near the earth’s surface is approximately 10-4 T. The more convenient unit of magnetic field strength is a gauss (1 G = 10-4 T).

The instrument used in this experiment is a tangent galvanometer that consists of 1-5 turns of wire oriented in a vertical plane that produce a horizontal magnetic field. The direction of the magnetic field at the center of the wire loop can be determined with the help of the right-hand-rule . If the curled fingers of the right hand are pointed in the direction of the current the thumb, placed at the center of the loop, indicates the direction of the magnetic field. The magnetic field of the coil is parallel to the coil axis.

Figure 1 shows the vector sum Bnet of the Earth's magnetic field (BEarth) and the magnetic field due to the current (BLoop) for the case when the coils of the galvanometer are oriented so that the Earth's magnetic field (BEarth) is parallel to the plane of the coils. The magnetic field due to the current (BLoop) being perpendicular to the coils plane will then be perpendicular to the Earth's field. Therefore the relationship between the horizontal component of the earth's magnetic field BEarth and the magnetic field of the coil BLoop can be expressed as

tanθ = BLoop / BEarth (2)

where θ is the angle between BEarth and Bnet. From equations (1) and (2) we get

(3)

This can be rewritten as

tan = M·N·I (4)
where = constant.

The horizontal component of the earth's field can now be found by measuring the field due to the coils and the direction of the net magnetic field relative to the direction of the earth's field. The angle θ can be found by using a compass. If the compass is first (with no current: I = 0) aligned with the magnetic field BEarth and then current is supplied to the coils, the compass needle will undergo an angular deflection θ. Because of the relationship given by equation (4) this equipment is called a tangent galvanometer. Note that for θ = 45o, tanθ = 1 and BLoop = BEarth.

θ

B Earth

B net

Figure 1. Vector sum of the magnetic fields.

B Loop

Objectives:

To verify:

· the vector nature of magnetic fields;

· that the field at the center of a current loop is normal to the loop and directed in accordance with right hand rule;

To investigate the relationship between the magnetic field and:

· the number of turns - B(N);

· the value of the current - B(I) inside a current carrying coil.

To determine the strength of the horizontal component of the Earth’s magnetic field.

Equipment:

Virtual Tangent Galvanometer with two views: Overhead and Oblique. Virtual DC power supply, ammeter and compass mounted in the center from the Tangent Galvanometer Apparatus lab (Magnetic Fields - The Tangent Galvanometer on the web site http://virtuallabs.ket.org/physics/ ); Logger Pro (LP) software. LP is available at MyASU > My Apps.

Procedure:

Before starting the experiment please get practice with the virtual equipment!

Log in to Virtual Physics Labs using your KET ID and password. Load the virtual “Tangent Galvanometer Apparatus Lab” and familiarize yourself with the setup.

The apparatus is viewed from two perspectives: Overhead (Figure 2a), and Oblique (Figure 2b).

You will switch between views using the buttons at the top left edge of the screens. Take some time to become familiar with each view.

In the Overhead view shown in Figure 2a, you see two vector arrows. One represents the horizontal component of the Earth’s magnetic field. The other represents the magnetic field produced by the current-carrying wire loops. Neither vector automatically points in the appropriate direction. Rather these vectors can be rotated as needed by dragging the points of the arrows. The entire apparatus can be rotated in the overhead view by dragging the Handle.

The coil unit has a compass mounted in the middle. With no current applied to the coil, the compass responds only to the horizontal component of the earth’s magnetic field.

Figure 2a. View 1: Overhead

Figure 2b. View 2: Oblique

The Oblique view shown in Figure 2b does not rotate. Explore the following in the Oblique view. A frame with a pair of vertical supports provides two nails which hold 1 to 5 circular loops of insulated wire.

A horizontal platform holds a sheet of polar graph paper for measuring angles in the horizontal plane. The compass at the bottom right provides a close - up of the real compass. You will take compass reading there. Remember that the red end of the compass is its north end (seeking Earth's North Pole). Notice how the deflection of the compass is affected by the power switch, the voltage adjust knob, and the number of loops of wire.