A metal bar of mass 500 g slides outward at a constant speed of 1.5 cm / s over two parallel rai

step 1 Hi, in the given problem there is a U -shaped metallic frame. This is the metallic frame over wh

A metal bar of mass 500 g slides outward at a constant speed...

A metal bar of mass 500 g slides outward at a constant speed of $1.5 \mathrm{cm} / \mathrm{s}$ over two parallel rails separated by a distance of $30 \mathrm{cm}$ which are part of a U-shaped conductor. There is a uniform magnetic field of magnitude $2 \mathrm{T}$ pointing out of the page over the entire area. The railings and metal bar have an equivalent resistance of $150 \Omega$ (a) Determine the induced current, both magnitude and direction. (b) Find the direction of the induced current if the magnetic field is pointing into the page. (c) Find the direction of the induced current if the magnetic field is pointed into the page and the bar moves inwards.

Key Concepts

Lorentz Force

The Lorentz force refers to the force experienced by a charged particle moving in a magnetic field. It is given by the cross product of the velocity of the charge and the magnetic field vector. This force is perpendicular to both the velocity of the charge and the direction of the magnetic field, and it is responsible for the separation of charges in a moving conductor, which is the basis for the generation of motional emf.

Motional EMF

This concept refers to the electromotive force (emf) generated in a conductor that is moving through a magnetic field. In such situations, the motion of the conductor causes the charges inside it to experience a magnetic force, which in turn creates a separation of charges and an induced voltage. The magnitude of this emf depends on factors such as the velocity of the motion, the magnetic field strength, the length of the conductor perpendicular to the field, and the angle between the direction of motion and the magnetic field.

Faraday’s Law of Induction

Faraday's Law states that an electromotive force is induced in a circuit when there is a change in the magnetic flux through the circuit. The induced emf is proportional to the rate of change of the flux, and its direction is determined by how the magnetic flux is changing. This law provides the foundational principle for understanding how electrical energy can be generated from mechanical motion or other changing magnetic conditions.

Lenz’s Law

Lenz’s Law is a principle that determines the direction of the induced current in a circuit. It states that the induced current will flow in such a way that its own magnetic field opposes the change in the original magnetic flux that produced it. Essentially, this is nature's way of conserving energy, ensuring that any change in the magnetic flux results in a counteracting force.

Resistive Circuit Analysis

In a resistive circuit, the induced current is determined by applying Ohm's law, which relates the voltage (or emf) to the current through the resistance in the circuit. Once the induced emf is calculated (using Faraday’s Law or motional emf concepts), it can be divided by the circuit’s resistance to determine the magnitude of the current. This analysis is crucial for practical applications where the circuit's resistance significantly affects the overall current flow.

Transcript

00:02 Hi, in the given problem there is a u -shaped metallic frame.

00:11 This is the metallic frame over which there is a metallic bar which is moving over these rails or two opposite sides of this frame with a speed of 1 .5 centimeter per second towards right here like this this speed can also be given as 1 .5 into 10 dash bar minus 2 meter per second mass of this bar has been given as 500 or 0 .5 kilogram but we think there is no use of this mass we'll see it later on the effective length of this metallic bar within the magnetic field is length l is equal to 30 centimeter or we can say this is 0 .3 meter and the magnetic field b is two tesla.

01:25 Here this magnetic field is perpendicular to the plane of paper and coming out of it.

01:38 Like this this magnetic field is coming out of the plane of paper perpendicularly resistance of this whole of the loop has been given as r is equal to 150 oom now in the first part of the problem we have to find the value of current induced in the loop which will be given by onso as emf divided by r where this emph epsilon is the motional whose expression is b into v into l divided by r so putting all these values here for b this is 2 or v this is 1 .5 into 10 dashed bar minus 2 meter per second for length this is 0 .3 and resistance is 150 om so finally the value of this current comes out to be 6 .0 into 10 based the power minus 5 am here this is the magnitude of the current induced in it now we have to find the sense the direction of this current also we have to determine the induced current both magnetine direction and direction of the induced current if the magnetic field is pointing into so in the first case the rod this metallic rod was moving for which we will use lemming's right hand rule as per this fleming's right hand rule the bar the metal bar is moving towards right so the thumb of our right hand will be kept will be stretched outward and the magnetic field is coming out so the forefinger will be stretched out of the plane of paper in doing this the middle finger will go down so this will be the direction of current induced so over overall, if we look into the loop, the direction of the current will become clockwise...

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