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1. The maximum magnetic field magnitude you are exposed to due to current in the electrical wiring in your house (E, K, P)

1. The maximum magnetic field magnitude you are exposed to due to current in the electrical wiring in your house (E, K, P)

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Developing a Feel Make an order-of-magnitude estimate of each of the following quantities. Letters in parentheses refer to hints below. Use them as needed to guide your thinking. 1. The maximum magnetic field magnitude you are exposed to due to current in the electrical wiring in your house (E, K, P) 2. The straight-wire current needed to reverse the deflection of a compass needle sitting on your laboratory table (H, A, O, W) 3. The maximum magnetic field strength 10 m from a typical light- ning bolt (G, R) 4. The maximum magnitude of the magnetic field you can produce in a solenoid sitting on your laboratory table when the core con- tains only air (D, N, Q, U) 5. The maximum magnetic force per meter between the antiparallel currents in your household wiring (P, E) 6. The electric current around the equator needed to produce Earth's magnetic field at the North Pole (B, I, M, S) 7. The magnitude of the magnetic field at the center of a Bohr-model hydrogen atom caused by the electron orbiting the nucleus (C, J, T) 8. The magnitude of the magnetic field at the North Pole that might be attributed to Earth's rotation, assuming a uniformly charged surface (F, L, I, V)
Transcribed Image Text:Developing a Feel Make an order-of-magnitude estimate of each of the following quantities. Letters in parentheses refer to hints below. Use them as needed to guide your thinking. 1. The maximum magnetic field magnitude you are exposed to due to current in the electrical wiring in your house (E, K, P) 2. The straight-wire current needed to reverse the deflection of a compass needle sitting on your laboratory table (H, A, O, W) 3. The maximum magnetic field strength 10 m from a typical light- ning bolt (G, R) 4. The maximum magnitude of the magnetic field you can produce in a solenoid sitting on your laboratory table when the core con- tains only air (D, N, Q, U) 5. The maximum magnetic force per meter between the antiparallel currents in your household wiring (P, E) 6. The electric current around the equator needed to produce Earth's magnetic field at the North Pole (B, I, M, S) 7. The magnitude of the magnetic field at the center of a Bohr-model hydrogen atom caused by the electron orbiting the nucleus (C, J, T) 8. The magnitude of the magnetic field at the North Pole that might be attributed to Earth's rotation, assuming a uniformly charged surface (F, L, I, V)
Hints A. What is the horizontal component of Earth's magnetic field in your neighborhood? B. What is the magnetic field magnitude at the North Pole? C. What is the orbit radius? U. What is the maximum number of turns n per meter ofsolenoid? V. How should you model the current? W. How close to the wire can you place the compass? D. What are the crucial variables to maximize? E. What is the current configuration? F. What is the magnitude of the electric field near Earth's surface? G. How should you model the current? H. How should the wire be oriented? I. What is the radius of Earth? J. What is the electron's speed? K. How close do you come to the wiring? L. What surface charge density could create this electric field magnitude? M. What is the straight-line distance from a point on the equator to the North Pole? Key (all values approximate) A. 2 x 10-5 T; B. 7 × 10-5 T; C. 5 × 10-1" m; D. because B = µonI, both I and n (number of windings per unit length) should be maximized; E. paired conductors separated by 10 m (two copper wires inside a nonconducting sheath) and carrying equal-magnitude currents in opposite directions; F. 100 V/m; G. approximately a vertical line; H. the compass detects horizontal magnetic fields, so orient the wire vertically; I. 6 X 10° m; J. electrical attraction provides centripetal force, so 2 x 10° m/s; K. 0.1 m if you stand near a wall; L. from Coulomb's law, 10° C/m²; M. 9 × 10³ km; N. laboratory tables are powered N. What maximum current is reasonable? O. What magnetic field strength is needed? P. What is the maximum likely current in each conductor? Q. What is a typical wire diameter used to carry currents of this magnitude in household or building wiring? R. What is the peak current? S. How can you compute the vector sum of the magnetic field mag- nitudes due to a large number of tiny segments of the current loop? T. What magnitude of charge does the electron carry, and what is its inertia? with 20 A, 120 V circuits, so the available current will be on the order of 20 A; O. enough to more than cancel Earth's magnetic field, say 4 X 10³T; P. 20 A for large appliances; Q. About 2 mm wire diameter; R. 105 A; S. by using the Biot-Savart law; T. e = 1.6 x 1019 C, m² = 9.11 × 10-31 kg; U. with 2-mm wire diameter, 500 turns per meter (or some small multiple of 500 turns per meter, if the wire is wound in more than one layer) are possible; V. as a stack of horizontal current loops of different radii (careful: current depends on radius); W. 0.02 m.
Transcribed Image Text:Hints A. What is the horizontal component of Earth's magnetic field in your neighborhood? B. What is the magnetic field magnitude at the North Pole? C. What is the orbit radius? U. What is the maximum number of turns n per meter ofsolenoid? V. How should you model the current? W. How close to the wire can you place the compass? D. What are the crucial variables to maximize? E. What is the current configuration? F. What is the magnitude of the electric field near Earth's surface? G. How should you model the current? H. How should the wire be oriented? I. What is the radius of Earth? J. What is the electron's speed? K. How close do you come to the wiring? L. What surface charge density could create this electric field magnitude? M. What is the straight-line distance from a point on the equator to the North Pole? Key (all values approximate) A. 2 x 10-5 T; B. 7 × 10-5 T; C. 5 × 10-1" m; D. because B = µonI, both I and n (number of windings per unit length) should be maximized; E. paired conductors separated by 10 m (two copper wires inside a nonconducting sheath) and carrying equal-magnitude currents in opposite directions; F. 100 V/m; G. approximately a vertical line; H. the compass detects horizontal magnetic fields, so orient the wire vertically; I. 6 X 10° m; J. electrical attraction provides centripetal force, so 2 x 10° m/s; K. 0.1 m if you stand near a wall; L. from Coulomb's law, 10° C/m²; M. 9 × 10³ km; N. laboratory tables are powered N. What maximum current is reasonable? O. What magnetic field strength is needed? P. What is the maximum likely current in each conductor? Q. What is a typical wire diameter used to carry currents of this magnitude in household or building wiring? R. What is the peak current? S. How can you compute the vector sum of the magnetic field mag- nitudes due to a large number of tiny segments of the current loop? T. What magnitude of charge does the electron carry, and what is its inertia? with 20 A, 120 V circuits, so the available current will be on the order of 20 A; O. enough to more than cancel Earth's magnetic field, say 4 X 10³T; P. 20 A for large appliances; Q. About 2 mm wire diameter; R. 105 A; S. by using the Biot-Savart law; T. e = 1.6 x 1019 C, m² = 9.11 × 10-31 kg; U. with 2-mm wire diameter, 500 turns per meter (or some small multiple of 500 turns per meter, if the wire is wound in more than one layer) are possible; V. as a stack of horizontal current loops of different radii (careful: current depends on radius); W. 0.02 m.
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