Ampere's Law
Introduction
In this experiment, we will verify Ampere's Law using a coil and a Giant MagnetoResistive or GMR sensor. A GMR sensor probe is a device which measures magnetic field strength. It has an output voltage which is proportional to magnetic field and input voltage.
Procedure
The coils used in this experiment have 1500 turns of copper magnet wire. Measure the resistance of the coil with an ohmmeter and the inner and outer diameters of the coil. Use the average diameter of the coil to calculate the expected value of the slope of the measured field versus coil voltage.
Use the function generator to supply the field sensor with 5.0 V DC offset and 0.0 V AC amplitude (set this voltage using the multimeter and connect the red and black wires of the sensor to the input). Use the multimeter to measure the DV voltage output of the sensor (blue and white wires).
Data Sheet
First we measure whether the magnet produces a field as strong as the equation would predict.
I. Measure the quantities for steps 1-5 below and calculate step 6.
1. Resistance of coil = R = ______
2. Inner diameter of coil = ______
3. Outer diameter of coil = ______
4. Average diameter of coil = 2a = ______
5. N = 1500
6. Theoretical value of = ______in
II. Place the sensor in the center of the coil and measure magnetic field for a coil voltage of 3 V --the coil voltage is supplied with the Pasco Power Supply.
With a 5.00 V input voltage the sensor has a calibration constant of 6.7 mT/Vout – use this to calculate the magnetic field values. Fill in the data in step 7 and calculate 8.
7.
Coil Voltage (V) / Coil Current (mA) / Sensor Voltage (mV) / Magnetic Field (mT)3.0
8. Experimental value of = ______
III. Now we test Ampere’s Law. Set the coil voltage to 3.0 V and measure the magnetic field at each of the alignment marks on the coil support. Place the sensor in the groove to perform this measurement. The sensor measures the component of the magnetic field along the length of the support, so this is equivalent to taking the dot product of the vectors of B and L. The sum of these measurements, multiplied by the increment of the displacement is a line integral around the enclosed current NI.
9.
Index / Sensor Voltage (mV) / Bi(mT)Ampere’s Law tells
The left side you just measured, only we replace the integral by a sum over discrete steps, i.e. the values of B you measured at each step times the step length.
10. ______
The right side [you also measured] is just that current in the coil you had “walked” around
11. ______