Concept explainers
(a)
The expression for the current in terms of
(a)
Answer to Problem 58AP
The expression for the current in terms of
Explanation of Solution
Write the expression to obtain the area enclosed between the bar and the two rails.
Here,
Write the expression to obtain the magnetic flux.
Here,
Substitute
Write the expression for induced emf based on Faraday’s law.
Here,
Substitute
Here,
Write the expression to obtain the magnitude of current induced in the bar.
Here,
Substitute
Therefore, the expression for the current in terms of
(b)
The analysis model that properly describes the moving bar when maximum power is delivered to the light bulb.
(b)
Answer to Problem 58AP
The bar moves with the constant velocity when maximum power is delivered to the light bulb. This constant velocity with which the bar is moving is due to the reason that the magnetic force is equal in magnitude to the applied force but they are opposite in direction. Thus this analysis model is similar model of particle in equilibrium.
Explanation of Solution
The analysis model that properly describes the moving bar when maximum power is delivered to the light bulb is similar to the model of particle in equilibrium that is when the resultant of all the forces is equal to zero. It means that the particle is in equilibrium.
The bar moves with the constant velocity when maximum power is delivered to the light bulb. This constant velocity with which the bar is moving is due to the reason that the magnetic force is equal in magnitude to the applied force but they are opposite in direction. Thus this analysis model is similar model of particle in equilibrium.
(c)
The speed with which the bar is moving when maximum power is delivered to the light bulb.
(c)
Answer to Problem 58AP
The speed with which the bar is moving when maximum power is delivered to the light bulb is
Explanation of Solution
Write the expression when maximum power is delivered to the light bulb.
Here,
Write the expression to obtain the applied force to the bar.
Here,
Compare equation (I) and (II).
Substitute
Here,
Conclusion:
Substitute
Therefore, the speed with which the bar is moving when maximum power is delivered to the light bulb is
(d)
The current in the light bulb when maximum power is delivered to it.
(d)
Answer to Problem 58AP
The current in the light bulb when maximum power is delivered to it is
Explanation of Solution
Consider equation (III).
Re-write the above equation.
Conclusion:
Substitute
Therefore, the current in the light bulb when maximum power is delivered to it is
(e)
The maximum power delivered to the light bulb.
(e)
Answer to Problem 58AP
The maximum power delivered to the light bulb is
Explanation of Solution
Write the expression to obtain the maximum power delivered to the light bulb.
Here,
Conclusion:
Substitute
Therefore, the maximum power delivered to the light bulb is
(f)
The maximum mechanical input power delivered to the bar by the applied force.
(f)
Answer to Problem 58AP
The maximum mechanical input power delivered to the bar by the applied force is
Explanation of Solution
Write the expression to obtain the maximum mechanical input power delivered to the bar by the applied force.
Here,
Conclusion:
Substitute
Therefore, the maximum mechanical input power delivered to the bar by the applied force is
(g)
Weather the speed found in part (c) change, if the resistance increases and all the other quantity remain same.
(g)
Answer to Problem 58AP
Yes, the speed found in part (c) change, if the resistance increases and all the other quantity remain same.
Explanation of Solution
Write the expression (IV) used in part (c) to determine the speed of the bar.
From the above expression, speed is directly proportional to the resistance. Thus, if the resistance increases than the speed is also increases if all the other quantity remains constant.
Therefore, the speed found in part (c) changes, if the resistance increases and all the other quantity remains the same.
(h)
Weather the speed found in part (c) increases or decreases if resistance increases and all the other quantities remain same.
(h)
Answer to Problem 58AP
The speed found in part (c) increases if resistance increases and all the other quantities remain same.
Explanation of Solution
Write the expression (IV) used in part (c) to determine the speed of the bar.
From the above expression, speed is directly proportional to the resistance.
Therefore, the speed found in part (c) increases if resistance increases and all the other quantities remain same.
(i)
Weather the power found in part (f) change if resistance increases as current increases.
(i)
Answer to Problem 58AP
Yes, the power found in part (f) changes if resistance increases as current increases.
Explanation of Solution
Write the expression used in part (f) to determine the speed of the bar.
From the above expression, power is directly proportional to the velocity and further velocity is directly proportional to the resistance.
Therefore, the power found in part (f) changes if resistance increases as current increases.
(j)
Weather the power found in part (f) is larger or smaller if resistance increases as current increases.
(j)
Answer to Problem 58AP
The power found in part (f) is smaller if the resistance increases as current increases.
Explanation of Solution
Write the expression used in part (f) to determine the speed of the bar.
From the above expression, power is directly proportional to the velocity and further velocity is directly proportional to the resistance.
Thus, power increase if resistance increases.
Therefore, the power found in part (f) is smaller if the resistance increases as current increases.
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Chapter 31 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- Consider the apparatus shown in Figure P30.32: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular and into the page. The distance between the horizontal rails is = 0.800 m. The resistance of the lightbulb is R = 48.0 , assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N. We wish to find the maximum power delivered to the lightbulb. (a) Find an expression for the current in the lightbulb as a function of B, , R, and v, the speed of the bar. (b) When the maximum power is delivered to the lightbulb, what analysis model properly describes the moving bar? (c) Use the analysis model in part (b) to find a numerical value for the speed v of the bar when the maximum power is being delivered to the lightbulb. (d) Find the current in the lightbulb when maximum power is being delivered to it. (e) Using P = I2R, what is the maximum power delivered to the lightbulb? (f) What is the maximum mechanical input power delivered to the bar by the force F? (g) We have assumed the resistance of the lightbulb is constant. In reality, as the power delivered to the lightbulb increases, the filament temperature increases and the resistance increases. Does the speed found in part (c) change if the resistance increases and all other quantities are held constant? (h) If so, does the speed found in part (c) increase or decrease? If not, explain. (i) With the assumption that the resistance of the lightbulb increases as the current increases, does the power found in part (f) change? (j) If so, is the power found in part (f) larger or smaller? If not, explain. Figure P30.32arrow_forwardA piece of insulated wire is shaped into a figure eight as shown in Figure P23.12. For simplicity, model the two halves of the figure eight as circles. The radius of the upper circle is 5.00 cm and that of the lower circle is 9.00 cm. The wire has a uniform resistance per unit length of 3.00 Ω/m. A uniform magnetic field is applied perpendicular to the plane of the two circles, in the direction shown. The magnetic field is increasing at a constant rate of 2.00 T/s. Find (a) the magnitude and (b) the direction of the induced current in the wire. Figure P23.12arrow_forwardWhy is the following situation impossible? A conducting rectangular loop of mass M = 0.100 kg, resistance R = 1.00 , and dimensions w = 50.0 cm by = 90.0 cm is held with its lower edge just above a region with a uniform magnetic field of magnitude B = 1.00 T as shown in Figure P30.34. The loop is released from rest. Just as the top edge of the loop reaches the region containing the field, the loop moves with a speed 4.00 m/s. Figure P30.34arrow_forward
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