The Magnetic Field inside a Solenoid

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Jeffry Stewart
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1 The Magnetic Field inside a Solenoid Theory The magnetic field surrounding a long straight wire is circumferential; it takes the form of concentric circles centered on the current. The direction of these field lines is given by the right-hand rule. If your thumb points in the direction of the current I, your fingers curl around the wire in the direction of the field. The magnitude of the field at a distance s fromthewireisgivenby µ o I B = Eqn. 1 2πs where µ o is the permeability of free space. As you can see from Eqn. 1, the field is stronger the more current there is in the wire or the closer you are to it. When a wire is in the form of a closed loop, the field lines around the wire will coincide at the center of the loop such that the field at this point will be perpendicular to the plane of the loop. Again, the right-hand rule gives direction. If you curl your fingers around the loop in the direction of the current I, your thumb will point in the direction of the field. Its magnitude is given by where r is the radius of the loop. µ o I B = Eqn. 2 2r If a coil is made by adding more loops of wire to the previous single loop, then the field becomes proportionally stronger with each additional loop; namely where N is the total number of loops in the coil. µ o NI B = Eqn. 3 2r A solenoid is essentially a long coil of wire. If its turns are close together and the radius of the loops small relative to the length, then the field within the solenoid is uniform and axial (except near the ends). The direction of the field is found with the right hand just as in the case of the single loop. The magnitude of the field inside the solenoid is given by B = µ o ni Eqn. 4 where n is the number of turns per unit length making up the solenoid. Again, the diameter of the solenoid does not matter provided it is small compared to its length. Additionally, Eqn. 4 demonstrates the relationship between the current I through a solenoid and the magnitude of the magnetic field B inside the solenoid due to this current. Apparatus Solenoid, Power supply, DMM, Wires, Computer with Pasco 750 interface and magnetic field sensor, Stand, Rule, Compass. Procedures Assemble the circuit shown in Figure 1, with the power supply, DMM, and solenoid in series. With the power supply off, rotate the solenoid so that its axis is perpendicular to the horizontal component of the earth s magnetic Page 1 of 5

2 field as shown on the compass. Make sure that the magnetic field sensor is set to measure axi al fields, then place the probe into the solenoid so that it extends down the center of the solenoid (along its axis). Turn on the power supply and vary the current in the solenoid from 0A up to a maximum of 2A. At each current, record its magnitude as well as the magnitude of the magnetic field as indicated by the field sensor. Place this data in Table 1. Current (A) Table 1 Magnetic Field (Gauss) Magnetic Field (T) Plot the Magnetic Field of the Solenoid (in T) as a function of the Current in the Solenoid. Analysis What type of curve did you obtain when you plotted the magnetic field as a function of the current? Does this confirm the relationship shown in Eqn. 4? If so, how? If not, why not? Page 2 of 5

3 Determine the slope of the curve in this graph, and record the value here, along with its units. Use Eqn. 4 and the slope just determined to calculate the number of turns per unit length n in the solenoid. Show all work here. Measure the length of the solenoid and record the value here. With the value of n obtained in the previous question, calculate the number of turns actually in the solenoid. Again, show all work. Why was it necessary to align the solenoid like you did in the procedure? Page 3 of 5

4 Pre-Lab: The Magnetic Field inside a Solenoid Name Course Section What is the magnitude of the magnetic field 1.0cm from a wire that carries a current of 1.0A? Suppose that the wire is perpendicular to this page and that the current is flowing into the page. What would the direction of the field be directly above the wire? A 10 turn circular coil of wire with diameter 5.0cm has a current of 0.25A flowing through it. What is the magnitude of the magnetic field at the center of the coil? The plane of the coil lies in the plane of this page and the current is flowing through the coil in a counterclockwise direction. What would be the direction of the field? A solenoid 20.0cm long with a diameter of 4.0cm consists of 300 turns. How many turns per unit length are in this solenoid? What happens to the magnitude of the magnetic field inside a solenoid when the current is doubled? Page 4 of 5

5 You wish to build a 10.0cm long solenoid that will have a magnetic field magnitude of 2.0mT inside it when the current through the solenoid is 3.0A. How many turns do you need? Page 5 of 5

FORCE ON A CURRENT IN A MAGNETIC FIELD

7/16 Force current 1/8 FORCE ON A CURRENT IN A MAGNETIC FIELD PURPOSE: To study the force exerted on an electric current by a magnetic field. BACKGROUND: When an electric charge moves with a velocity v