Repeat Problem 42 if the magnetic field is 2.5 T to the left (in the -x -direction).

Name: Problem 43, Chapter 19: College Physics
Uploaded: 2021-08-17T16:24:31-08:00
Duration: 7 min 22 s
Channel: Vishal Gupta
Description: Repeat Problem 42 if the magnetic field is 2.5 T to the left (in the -x -direction).

Repeat Problem 42 if the magnetic field is 2.5 T to the...

Key Concepts

Magnetic Field

A magnetic field is a vector field that exerts a force on moving charges and magnetic dipoles. Its magnitude and direction determine the behavior of charged particles in its influence. In problems dealing with magnetic fields, understanding its vector nature is essential, as it influences the resultant force through both its strength and orientation in space.

Lorentz Force

The Lorentz force is the combined electric and magnetic force acting on a charged particle, but in a context where only a magnetic field is involved, it is defined as F = q(v × B). This cross product implies that the force is perpendicular to both the velocity of the particle and the magnetic field, determining the particle's curved trajectory. Understanding how to use and interpret this formula is critical when analyzing particle motion in magnetic environments.

Vector Direction and Cross Product

In problems involving magnetic fields, correctly determining the direction of forces and motion often relies on vector operations such as the cross product. This requires careful attention to coordinate systems and the right-hand rule, ensuring that the signs and directions of vectors like the magnetic field and velocity are accurately accounted for. Such understanding is fundamental in predicting the behavior of charged particles under magnetic influences.

Charged Particle Motion in Magnetic Fields

The motion of a charged particle in a magnetic field typically involves circular or helical trajectories due to the continuous perpendicular force acting on the particle. Analyzing this motion involves understanding how factors like the charge magnitude, velocity, magnetic field strength, and particle mass determine the radius and period of the resultant path. This concept is pivotal in numerous applications ranging from cyclotrons to astrophysics.

Transcript

00:01 Hi, in the given problem, first of all, there is a rectangular current carrying coil.

00:10 The directions are given as upward in the plane of paper.

00:15 This is y, x, and towards right, this is the x -axis.

00:24 Magnetic field passing through this coil is perpendicular to the plane of paper and coming out of it means simply we can say magnetic field is along positive xxas in the first part of the problem the values given are for magnetic field this is 2 .5 tesla and sorry in this problem the magnetic field is not upward out of the plane of paper actually this magnetic field is two words left means along negative x x x.

01:08 So the magnetic field is having the same magnitude as 2 .5 tesla, but this is to the left.

01:22 Means if we draw the magnetic field lines here this is the magnetic field which is directed along negative xxas and having the magnitude 2 .5 tesla.

01:42 Now as and one more thing the length of this loop is given as 30 centimeter and its width is given as 20 centimeter.

02:00 Now using the expression for magnetic force experienced by a straight current carrying conductor kept in a magnetic field that is given as f is equal to i l cross b cross product of current element with the magnetic field or it will be given by in magnitude it is i lb sine theta so for the upper arm as the direction of current is clockwise this is the direction of current and the magnitude of current and the magnitude of current current that is also given to us and this is just 1 .0 ampere.

03:00 So for the upper arm, the angle between current element which is towards right means along positive x -axis and the magnetic field which is towards left means along negative x -axis.

03:14 So for the upper arm angle will be 180 degree.

03:19 So the force experienced by the upper arm will be i.

03:26 L .b...

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