(II) While demonstrating Faraday’s law to her class, a physics professor inadvertently moves the gold ring on her finger from a location where a 0.80-T magnetic field points along her finger to a zero-field location in 45 ms. The 1.5-cm-diameter ring has a resistance and mass of 55 μ Ω and 15 g, respectively. ( a ) Estimate the thermal energy produced in the ring due to the flow of induced current. ( b ) Find the temperature rise of the ring, assuming all of the thermal energy produced goes into increasing the ring’s temperature. The specific heat of gold is 129 J/kg·C°.
(II) While demonstrating Faraday’s law to her class, a physics professor inadvertently moves the gold ring on her finger from a location where a 0.80-T magnetic field points along her finger to a zero-field location in 45 ms. The 1.5-cm-diameter ring has a resistance and mass of 55 μ Ω and 15 g, respectively. ( a ) Estimate the thermal energy produced in the ring due to the flow of induced current. ( b ) Find the temperature rise of the ring, assuming all of the thermal energy produced goes into increasing the ring’s temperature. The specific heat of gold is 129 J/kg·C°.
(II) While demonstrating Faraday’s law to her class, a physics professor inadvertently moves the gold ring on her finger from a location where a 0.80-T magnetic field points along her finger to a zero-field location in 45 ms. The 1.5-cm-diameter ring has a resistance and mass of 55 μΩ and 15 g, respectively. (a) Estimate the thermal energy produced in the ring due to the flow of induced current. (b) Find the temperature rise of the ring, assuming all of the thermal energy produced goes into increasing the ring’s temperature. The specific heat of gold is 129 J/kg·C°.
(b) Write down the statement and mathematical form of Faraday's Law of
magnetic induction.
(c) A coil 4.00 cm in radius, containing 500 turns, is placed in a uniform
magnetic field that varies with time according to
B = (0.0120 T/s)t + (3.00 × 10-5 T/s)t“
where t is time in seconds and T and s represents the units Tesla and
seconds, respectively.
The coil is connected to a 600-N resistor, and its plane is perpendicular
to the magnetic field. You can ignore the resistance of the coil.
[c.1] Find the magnitude of the induced emf in the coil as a function
of time.
[c.2] What is the current in the resistor at time t = 5.00 s?
2
An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. His wedding ring has a diameter of 2.2 cm and it takes 0.425 s to move it into the field.
(a) What average current is induced in the ring in A if its resistance is 0.0100 Ω?
(b) What average power is dissipated in mW? (c) What magnetic field is induced at the center of the ring in T?
Chapter 29 Solutions
Physics for Scientists and Engineers with Modern Physics
University Physics with Modern Physics (14th Edition)
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