Motional emf problem on inclined plane

In summary, a straight horizontal rod with a mass of 71 g is sliding down parallel conducting rails at an angle of 30 degrees, forming a closed rectangular loop. There is a uniform vertical magnetic field throughout the region and no friction or air drag acting on the rod. The goal is to find the current through the resistor when the rod's velocity is 4.6m/s (answer in mA) and the terminal velocity of the rod. This problem can be approached using the equations for magnetic force and induced emf, as well as the concept of magnetic flux.
  • #1
yankans
12
0

Homework Statement



a straight horizontal rod slides along parallel conducting rails at an angle with the horizontal of 30 degrees (inclined plane). The rails are connected at the bottom by a horizontal rail so that the rod and rails form a closed rectangular loop. A uniform vertical field exists throughout the region.
assume: rod remains in contact w/ rails as it slides down rails. rod experiences no friction/air drag. Rails and rod have negligible resistance. g = 9.8m/s^2.
a)if velocity of the rod is 4.6m/s, what is the current through the resistor? answer in mA.
b) what is the terminal velocity of the rod? (in m/s)

note: this is like a motional emf problem - the rod on rails
and
rod = 71 g in mass, moving at 4.6m/s
magnetic field = 0.16 straight down
resistor = 6.8 ohms


Homework Equations



F magnetic field = IBl where l is lowercase L, the width btwn rails
Emf = Blv
magnetic flux = Blx


The Attempt at a Solution



I honestly have no idea where to start this problem...
 
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  • #3


I would first break down the problem into smaller parts and analyze each part separately. Firstly, I would calculate the force of the magnetic field on the rod using the formula F = IBl. From the given information, I can calculate the value of B, the magnetic field, which is 0.16 T. I can also calculate the value of l, the width between the rails, using the given angle of 30 degrees and the mass of the rod. With these values, I can calculate the force of the magnetic field on the rod.

Next, I would use the formula for motional emf, Emf = Blv, to calculate the emf induced in the loop. This emf can also be seen as the voltage across the resistor, which can then be used to calculate the current through the resistor using Ohm's Law.

To determine the terminal velocity of the rod, I would use the equation for magnetic flux, Blx, where x is the distance that the rod has traveled along the rails. I would set this value equal to the motional emf calculated previously and solve for x. This would give me the distance that the rod needs to travel in order to reach its terminal velocity.

Finally, I would use the formula for acceleration, a = F/m, to calculate the acceleration of the rod. Knowing the acceleration and the initial velocity, I can use the equation v^2 = u^2 + 2as to calculate the terminal velocity of the rod.

In conclusion, this problem involves applying principles of magnetism, electromagnetism, and mechanics to calculate the current through a resistor and the terminal velocity of a rod sliding down an inclined plane.
 

What is motional emf on an inclined plane?

Motional emf on an inclined plane refers to the induced voltage or electromotive force (emf) that is created when a conductor moves along an inclined plane in the presence of a magnetic field. This phenomenon is also known as the Faraday's Law of Induction.

How is the magnitude of motional emf on an inclined plane calculated?

The magnitude of motional emf on an inclined plane can be calculated using the formula: emf = B*l*v*sin(theta), where B is the strength of the magnetic field, l is the length of the conductor, v is the velocity of the conductor, and theta is the angle of inclination.

What factors affect the motional emf on an inclined plane?

The strength of the magnetic field, the length of the conductor, the velocity of the conductor, and the angle of inclination are the main factors that affect the motional emf on an inclined plane. Additionally, the resistance of the conductor and the shape of the conductor may also have an impact on the induced emf.

What is the direction of the induced current in a motional emf problem on an inclined plane?

The direction of the induced current in a motional emf problem on an inclined plane can be determined by using the right-hand rule. If the motion of the conductor is perpendicular to the magnetic field, the induced current will be in the opposite direction of the motion. If the motion is parallel to the magnetic field, the induced current will be in the same direction as the motion.

What is the significance of studying motional emf on an inclined plane?

Studying motional emf on an inclined plane helps to understand the relationship between magnetic fields and induced currents. It also has practical applications in various technologies, such as generators and motors, where the motion of conductors is used to generate electricity. Additionally, it helps to explain the working principle of devices like speakers and microphones that use the motion of conductors in a magnetic field to produce sound.

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