Two horizontal metal rails are separated by 1.5 m and connected at their ends by a 3.0-Ωresistor

step 1 In this case what is happening is I have two parallel rods. They are connected by a resistor, by

Two horizontal metal rails are separated by 1.5 m and...

Two horizontal metal rails are separated by 1.5 $\mathrm{m}$ and connected at their ends by a $3.0-\Omega$ resistor to form a long, thin U shape. A metal axle with metal wheels on each side rolls along the rails at a speed of 25 $\mathrm{m} / \mathrm{s}$ . Earth's $\vec{B}$ field has a magnitude of $5.0 \times 10^{-5} \mathrm{T}$ and tilts downward $68^{\circ}$ below the horizontal. Make a list of the physical quantities you can determine using this information and determine two of them.

Two horizontal metal rails are separated by 1.5 $\mathrm{m}$ and connected at their ends by a $3.0-\Omega$ resistor to form a long, thin U shape. A metal axle with metal wheels on each side rolls along
the rails at a speed of 25 $\mathrm{m} / \mathrm{s}$ . Earth's $\vec{B}$ field has a magnitude of $5.0 \times 10^{-5} \mathrm{T}$ and tilts downward $68^{\circ}$ below the horizontal. Make a list of the physical quantities you can determine using this information and determine two of them.

Key Concepts

Lorentz Force

The Lorentz force represents the force experienced by a charged particle or a current-carrying conductor when it moves within a magnetic field. In conductive systems, this force is responsible for effects such as magnetic braking or the deflection of moving charges and is calculated as the vector cross product of the current element and the magnetic field.

Induced Current

Induced current is the electrical current that flows in a circuit due to an induced EMF, as described by Faraday's Law. Once an EMF is generated, Ohm's Law can be applied to determine the current by dividing the induced voltage by the circuit's resistance. This concept connects the electrical response (current) to the mechanical motion in the presence of a magnetic field.

Resistive Power Dissipation

Resistive power dissipation refers to the conversion of electrical energy into heat in a resistor when current flows through it. The power dissipated can be calculated using the relation P = I²R or P = V²/R, which is essential when considering energy losses in electrically induced systems.

Faraday's Law of Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (EMF) in that circuit. This principle is fundamental in electromagnetic induction and explains how movements of conductors in a magnetic field, or changing magnetic fields, produce electrical energy in a closed loop.

Motional EMF

Motional EMF is the voltage difference generated across a conductor moving through a magnetic field. It depends on the speed of the movement, the strength of the magnetic field, and the length of the conductor within the field. This concept is used to calculate the induced EMF when a conductor moves in a magnetic field.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a given area. It is the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field and the area's normal direction. This concept is central to understanding how changes in a magnetic field or the orientation of the area lead to phenomena like electromagnetic induction.

Transcript

00:06 In this case what is happening is i have two parallel rods.

00:12 They are connected by a resistor, by a resistor r.

00:20 The distance between the rods are l and a metal cart moves in this direction with a speed of v.

00:43 So we have to figure out what the area is over here and other than that, there's a magnetic field.

00:54 The magnetic field, this is the top view of the of my setup.

01:02 Now if i look at the side view of the setup then you will realize that if this is the horizontal, magnetic field is 68 degree below horizontal.

01:19 So this is the magnetic field and the vertical component of the magnetic field will be given by.

01:25 B sine 68 degree using the value of b to be 5 times 10 to the minus 5 tesla multiplied by sine 68 is 0 .93 and that comes out to be 4 .64 4 .6 4 times 10 to the minus 5 tesla.

02:57 So let us call this b perpendicular.

03:05 Now in this particular case what's happening is b perpendicular b perpendicular goes into the plane just because the area through which the magnetic field passes is reducing, the flux is changing and there will be an emf induced in the system let us tell let us first find the emf induced emf equals we don't care about the direction at this point negative d fee dt be perpendicular dot area or multiplied by area now let us assume that the rod moves to the right by an amount of x which makes the whole area to be oh by the way we can call this to be l prime the horizontal distance to be l prime so the area becomes the vertical l and the horizontal l prime l l now if you look at the system carefully you should be able to understand that the perpendicular value of magnetic field is constant, l stays constant, and dl prime, d t is l prime is on the time -dependent term, and the rate of change of l -prime is simply given by v.

05:27 So, p perpendicular, l -v.

05:33 Let us just put the numbers in now...

Please give Ace some feedback