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# Lab6 - Ampere's Law Purpose To investigate Ampere's Law by...

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Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral board, DC power supply with built-in voltmeter/ammeter, cables, Hall Effect magnetic sensor, meter stick Introduction Ampere's Law states that the line integral of B and d l over a closed path is 0 times the current enclosed in that loop: B dl = 0 I enclosed You have seen the usefulness of the law in determining, without complicated integration, the magnetic field merely by knowing the currents enclosed by a path with a high degree of symmetry, such as a circular loop around a long straight wire. For such a wire, the magnetic field is given by: B long straight wire = 0 I 2 R

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(For a long straight wire carrying current I the B field line direction is tangent to centered circles. Along those circles, B is constant, so we can “pull it out of the integral”. The remaining integral is simply the circumference of the circle, which is 2 R , so B long straight wire 2 R = 0 I ) In your experiment, I must be understood as NI multimeter since the single wire of the solenoid contributes I to the enclosed current with each winding (turn) of the solenoid) : B dl = 0 N I = 0 N I multimeter in general. Equation 1 If there is no net current within the closed path, the closed integral is zero. This does not necessarily mean there is no B field present along the line integral, or no currents enclosed. Rather it means that the dot product with the field direction sums to zero. Note that “Up” and “down” currents through the enclosed surface must be assigned opposite signs. Think of two adjacent wires with equal and opposite currents. The closed line integral surrounding them is zero. If the closed line integral is not zero, you know that there is a net current within the closed path which is generating a magnetic field. In this lab you will actually sum up the contributions of B · d l over such a path around a solenoid, to check if their sum does indeed equal 0 times the current enclosed by your path. The magnetic field around the solenoid will be determined by a magnetic sensor; you will measure the output voltage of the sensor (which is proportional to B) using the Fluke multimeter. The current through the solenoid will be measured by the readout on the power supply. SOLENOIDS An application of Ampere’s Law involves a solenoid (a wire coil wound on a cylinder) with: N = number of turns of solenoid (dimensionless) R = radius of coil (meters) I multimeter = current through solenoid (amperes) L = length of solenoid (meters). The B field intensity at the center
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Lab6 - Ampere's Law Purpose To investigate Ampere's Law by...

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