Review Electric current i is the net charge passing a given point in a given time i Physics for Scientists Engineers 2 dq dt The ampere is abbreviated as A and is given by 1A Spring Semester 2005 Lecture 33 1C 1s The current per unit area flowing through a conductor is the current density Midterm 2 Review J March 22 2005 Physics for Scientists Engineers 2 1 March 22 2005 Physics for Scientists Engineers 2 Review 2 Review 3 The property of a particular device or object that describes it ability to conduct electric currents is called the resistance R If the current is constant and perpendicular to the surface then and we can write an expression for the magnitude of the current density i J A The resistance R of that conductor is define as The current density and the drift velocity are parallel vectors pointing in the same direction and we can write J ne vd R Physics for Scientists Engineers 2 V i The unit of resistance is the ohm The property of a material that describes its ability to conduct electric currents is called the resistivity March 22 2005 2 1 3 March 22 2005 1V 1A Physics for Scientists Engineers 2 4 Review 4 Review 5 The resistance R of a device is given by The temperature dependence of the resistance of metals is given by L R A R R0 R0 T T0 is resistivity of the material from which the device is constructed R is the resistance at temperature T L is the length of the device R is the resistance at temperature T0 A is the cross sectional area of the device is the temperature coefficient of electric resistivity for the material under consideration The temperature dependence of the resistivity of metals is given by Ohm s Law for a circuit consisting of a resistor and a battery is given by 0 0 T T0 Vemf iR is the resistivity at temperature T 0 is the resistivity at temperature T0 Vemf is the emf or voltage produced by the battery is the temperature coefficient of electric resistivity for the material under consideration R is the resistance of the resistor March 22 2005 Physics for Scientists Engineers 2 i is the current 5 March 22 2005 Physics for Scientists Engineers 2 Review 6 6 Review 7 n resistors in series can be replaced by an equivalent resistance given by the sum of the resistances of the resistors in series We can visualize a circuit with a battery and a resistor in three dimensions n Req Ri i 1 n resistors in parallel can be replaced by an equivalent resistance given by the sum of the resistances of the resistors in parallel n 1 1 Req i 1 Ri The power dissipated in a circuit or circuit element is given by P iV i 2 R March 22 2005 Physics for Scientists Engineers 2 7 March 22 2005 V2 R Physics for Scientists Engineers 2 8 Review 8 Review 9 The force that a magnetic field exerts on a charge moving with velocity v is given by The unit of magnetic field strength the tesla T Ns N 1T 1 1 Cm Am The magnitude of the force exerted by a magnetic field on a moving charge is Another unit of magnetic field strength that is often used but is not an SI unit is the gauss G FB qv B 1 G 10 4 T 10 kG 1 T Typically the Earth s magnetic field is about 0 5 G at the surface FB qvBsin If the charge moves perpendicular to the magnetic field then The NSCL K1200 superconducting cyclotron has a magnetic field of 5 5 T F qvB March 22 2005 Physics for Scientists Engineers 2 9 March 22 2005 Review 10 mv qB For the same conditions we can relate the momentum p and the charge q to the magnitude of the magnetic field B and the radius r of the circular motion Br March 22 2005 10 Review 11 A charged particle with charge q and mass m moving with speed v perpendicular to a constant magnetic field with magnitude B will travel in a circle with radius r given by r Physics for Scientists Engineers 2 If we run a current i through a conductor of width h in a constant magnetic field B we induce a voltage VH across the conductor that is given by B VH VH dhne VH hne dv di i where n is the number of electrons per unit volume and e is the charge of an electron p q Hall Effect Physics for Scientists Engineers 2 11 March 22 2005 Physics for Scientists Engineers 2 12 Review 12 Review 13 0 is the magnetic permeability of free space whose value is Tm 0 4 10 7 A Ampere s Law is B ds 0ienc The magnitude of the magnetic field at a distance r from a long straight wire carrying currrent i is given by where the integral is carried out around an Amperian loop and ienc is the current enclosed by the loop B r 0i 2 r The magnitude of the magnetic field inside a long wire with radius R carrying a current i at a radius r is given by The magnitude of the magnetic field at the center of a loop with radius R carrying current i is given by i B 0 2R March 22 2005 Physics for Scientists Engineers 2 13 i B r 0 2 r 2 R March 22 2005 Review 14 We define the magnitude of the magnetic dipole moment of a coil to be NiA 0i1i2 L 2 d We can express the torque on a coil in a magnetic field as B The torque exerted by a magnetic field on a current carrying loop is given by Physics for Scientists Engineers 2 n i The magnetic potential energy of a magnetic dipole in a magnetic field is given by U B B cos iABsin March 22 2005 14 Review 15 The force between two currentcarrying wires is given by F12 Physics for Scientists Engineers 2 15 March 22 2005 Physics for Scientists Engineers 2 16 Review 16 Review 17 The magnetic field inside an ideal solenoid is given by Faraday s Law of Induction in words is The magnetic field inside an ideal toroidal magnet is given by Faraday s Law of Induction in equation form is The magnitude of the Vemf induced in a conducting loop is equal to the time rate of change of the magnetic flux from the loop This induced emf tends to oppose the flux change B 0in B Vemf 0 Ni 2 r d B dt Vemf is the induced voltage d B dt is time rate change of the magnetic flux The negative sign means that the induced voltage opposes the change in flux March 22 2005 Physics for Scientists Engineers 2 17 March 22 2005 Physics for Scientists Engineers 2 Review 18 Review 19 If we have a flat loop we can keep two of the three variables A B constant and …
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