A 2.00 -m length of wire is held in an east-west direction...

A 2.00 -m length of wire is held in an east-west direction and moves horizontally to the north with a speed of 15.0 $\mathrm{m} / \mathrm{s}$ . The vertical component of Earth's magnetic field in this region is 40.0$\mu \mathrm{t}$ directed downward. Calculate the induced emf between the ends of the wire and determine which end is positive.

Key Concepts

Right-Hand Rule

The right-hand rule is a method used to determine the direction of the force acting on positive charges in a conductor moving through a magnetic field. By pointing the fingers of the right hand in the direction of the velocity and curling them towards the direction of the magnetic field, the thumb points in the direction of the induced force or positive current. This helps in establishing which end of the conductor will acquire a positive charge.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving electric charges and magnetic dipoles. In this context, the magnetic field is provided by Earth, and its vertical component is crucial for calculating the induced EMF in a moving conductor. The field’s direction and magnitude directly affect the magnitude and polarity of the induced electric potential through the motion of the conductor through the field.

Motional EMF

Motional electromotive force (EMF) is generated when a conductor moves through a magnetic field, causing the free charges inside it to experience a force. This interaction between motion and magnetism leads to a separation of charges along the conductor, which produces a potential difference. The magnitude of the induced EMF is determined by the product of the magnetic field strength, the length of the conductor, and the component of the velocity perpendicular to the magnetic field.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field and is given by the equation F = q(v × B). This force is responsible for the separation of charges in the moving conductor, which in turn generates the motional EMF. Charges in the conductor are deflected according to the cross product of the velocity and the magnetic field vectors.

Transcript

00:01 We're told that we have a wire with a length l of two meters held in the east -west direction, and it moves horizontally at a velocity v of 15 meters per second.

00:11 And the vertical component of the earth's magnetic field in this region is 40 -mikrotestla or 40 times 10 to the minus 6 tesla.

00:20 So this is the perpendicular magnetic field because it's perpendicular to the motion or perpendicular to the motion or the velocity of the wire.

00:30 Okay, and we're asked here to calculate the induced emf between the ends of the wire and determine which end of the wire is positive.

00:39 Okay, so the earth's vertical component acting downward and the velocity on the wire is northward direction.

00:46 Therefore, the angle between the magnetic field and the velocity of the wire is 90 degrees.

00:50 So the expression for the emotional emf when the magnetic field is perpendicular to the velocity of the wire can be given as emf is equal to the perpendicular magnetic field times the length of the wire times the velocity.

01:12 Okay.

01:13 Well, we know all of these values here, so therefore we can go ahead and just plug them in, and it comes out to be 1 .2 times 10 to the minus 3, and the units here are volts.

01:31 Okay, so we can go ahead and box that in as the solution to the magnitude of the induced dmf.

01:38 But we're also asked to figure out which end is the positive end.

01:43 So use the right -hand rule to identify the direction of the magnetic force.

01:47 From the right -hand rule, the fingers represent the direction of motion of the object or the velocity...

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