An electromagnetic rail gun can fire a projectile using a...

An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two horizontal conducting rails that are $0.500 \mathrm{m}$ apart with a $50.0 \mathrm{g}$ conducting projectile that slides along the two rails. A magnetic field of $0.750 \mathrm{T}$ is directed upward. A constant current of $2.00 \mathrm{A}$ passes through the projectile. (a) What direction is the force on the projectile? (b) If the coefficient of kinetic

Key Concepts

Lorentz Force

The Lorentz force describes the force that a charged particle or a current-carrying conductor experiences in the presence of a magnetic field. This force is fundamental in electromagnetism and is given by the cross product of the current element and the magnetic field, resulting in a force that is perpendicular to both the direction of the current and the magnetic field.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the force that acts on a current-carrying conductor placed within a magnetic field. By orienting the thumb in the direction of current, the index finger in the direction of the magnetic field, the middle finger then points in the direction of the force, providing an intuitive way to apply vector cross-product principles.

Kinetic Friction

Kinetic friction is the resistive force that occurs when two surfaces slide against each other. It is characterized by a coefficient that, when multiplied by the normal force, determines the magnitude of the frictional force opposing motion. This concept is crucial in analyzing situations where objects experience resistance while in motion.

Electromagnetic Railgun Principles

Electromagnetic railguns operate by converting electrical energy into kinetic energy using electromagnetic forces. In these systems, a high current is passed through a projectile that bridges two conductive rails, and in the presence of a magnetic field, the Lorentz force accelerates the projectile. This concept integrates principles from both electromagnetism and mechanics to achieve high speeds.

Transcript

00:01 In the given problem there is a rail gun experiment which is having two parallel rails, metallic rails which are kept parallel to each other in a horizontal plane.

00:20 There is a metallic projectile rod which is free to slide over these two rails.

00:29 There is a source of voltage applied across these two rails and a magnetic field in the region vertically up like this the uniform magnetic field the gap between the rails which will serve as the length of projectile rod this gap is given as l is equal to 0 .550 meter and mass of the projectile rod that is given as 50 gram and magnitude of this magnetic field which is vertically upward this is given as 0 .750 tesla.

01:55 And finally, current passing through this circuit, rectangular circuit, which is in a direction as shown in the figure.

02:06 This current is having a magnitude 2 .0 ampere.

02:14 Now in the first part of the problem we have to find the direction of magnetic force experienced by this projectile rod which we find using.

02:27 Using fleming's left hand rule, either using fleming's left hand rule, by using right -hand screw rule in the expression for this magnetic force.

02:55 That expression for the magnetic force in vector form is f bar is equal to il cross b bar.

03:02 So we can use screw rule also right hand screw rule over this cross product.

03:08 So using either of the two rules, the direction of force experienced by the projectile rod comes out to be towards right along the rails for the rails for this.

03:55 We can say this is a wave from the battery...

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