Circular conductor with changing T effecting power and magnetic field

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SUMMARY

The discussion centers on the effects of temperature changes on a circular copper conductor's power dissipation and magnetic field strength. When the temperature of the conductor increases from T_1 to T_2, the rate of thermal energy dissipation changes from P_1 to P_2, and the magnetic field strength changes from B_1 to B_2. The correct relationship established is that B_1 < B_2 and P_2 > P_1, confirming that increased temperature enhances both power dissipation and magnetic field strength in an ohmic conductor.

PREREQUISITES
  • Understanding of ohmic conductors and their properties
  • Knowledge of thermal energy dissipation in conductors
  • Familiarity with the relationship between temperature and electrical conductivity
  • Basic principles of electromagnetism, particularly magnetic fields generated by current
NEXT STEPS
  • Research the equation for conductivity of metals as a function of temperature
  • Study the relationship between current, voltage, and magnetic fields in conductors
  • Explore the principles of Joule heating and its effects on electrical components
  • Investigate the behavior of copper conductors under varying thermal conditions
USEFUL FOR

Students studying electromagnetism, electrical engineers, and physicists interested in the thermal and magnetic properties of conductors.

Helmholtz
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Homework Statement



When we keep a circular copper (ohmic) conductor at a constant temperature T_1, thermal energy is produced along it at a rate P_1 and the magnetic field at its center has magnitude B_1. Then, we heat the conductor to a higher constant temperature T_2 (i.e. T_2>T_1). At temperature T_2, let P_2 and B_2 be the rate of dissipation of energy and the magnitude of the magnetic field at its center respectively. Which of the following is TRUE, if ALL other factors remain the same?

(A) It holds that B_1<B_2 and P_2=P_1.
(B) It holds that B_1>B_2 and P_2<P_1.
(C) It holds that B_1=B_2 and P_2=P_1.
(D) It holds that B_1<B_2 and P_2>P_1.
(E) It holds that B_1=B_2 and P_2>P_1.

Homework Equations



Not really sure

The Attempt at a Solution



Looking for a starting point
 
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Helmholtz said:

Homework Statement



When we keep a circular copper (ohmic) conductor at a constant temperature T_1, thermal energy is produced along it at a rate P_1 and the magnetic field at its center has magnitude B_1. Then, we heat the conductor to a higher constant temperature T_2 (i.e. T_2>T_1). At temperature T_2, let P_2 and B_2 be the rate of dissipation of energy and the magnitude of the magnetic field at its center respectively. Which of the following is TRUE, if ALL other factors remain the same?

(A) It holds that B_1<B_2 and P_2=P_1.
(B) It holds that B_1>B_2 and P_2<P_1.
(C) It holds that B_1=B_2 and P_2=P_1.
(D) It holds that B_1<B_2 and P_2>P_1.
(E) It holds that B_1=B_2 and P_2>P_1.

Homework Equations



Not really sure

The Attempt at a Solution



Looking for a starting point

You really need to show some effort when posting a question here. At least in your other threads so far, you've shown a bit of effort. Normally this thread would get deleted with a warning, but instead I'll ask a question to try to get you started.

What is the equation for the conductivity of metal versus temperature? That should be enough of a hint to allow you to solve this question.
 
BTW, do they specify *how* they are heating the wire? Is it connected to a constant voltage source to produce the current that makes the B field?
 

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