# Motion of a charge in a magnetic field

• harini_5
In summary, the conversation discusses the motion of a particle with charge q and mass m, starting from the origin with initial velocity u=a i. A uniform magnetic field of B=b/4 i + (sin 60)/2 j is present in space. When the z coordinate of the particle reaches its maximum, the component of velocity in the y direction is to be found. The discussion also mentions the role of magnetic force and its effect on the velocity.
harini_5
A particle of charge q and mass m starts its motion from origin with u=a i.A uniform B=b/4 i + (sin 60)/2 j exists everywhere in space.Find the component of velocity in y direction when z coordinate of it becomes maximum

Sir, if I find the magnetic force,Its component is 0 in Y direction.With no force acting in Y direction ,how come its velocity changes??

then I thought that

I'm missing one step:the force is in z direction initially but when it starts going in a circular motion then the x component of the field will cross with velocity and produce a force which has a component in y direction.

Treat your velocity as some unknown function of time: $\vec{u}(t)=u_x(t)\hat{i}+u_y(t)\hat{j}+u_z(t)\hat{k}$. Then use the expression for the magnetic field and the Lorentz force law to find the equation of motion for the particle. Then solve that differential equation for $\vec{u}(t)$ and plug in the initial condition $\vec{u}(0)=a\hat{i}$. Finally, find where the maximum of the z-component occurs.

## What is the motion of a charge in a magnetic field?

The motion of a charge in a magnetic field is affected by the Lorentz force, which is the force experienced by a charged particle moving through a magnetic field. This force is always perpendicular to both the direction of motion and the direction of the magnetic field.

## How does the direction of the magnetic field affect the motion of a charge?

The direction of the magnetic field determines the direction of the Lorentz force. If the magnetic field and the velocity of the charged particle are parallel, the force will be zero. If they are perpendicular, the force will be at a maximum and will cause the particle to move in a circular path.

## What is the relationship between the strength of the magnetic field and the force on a charged particle?

The strength of the magnetic field directly affects the force on a charged particle. A stronger magnetic field will result in a greater force on the particle, while a weaker field will result in a weaker force. This relationship can be described by the equation F = qvB, where F is the force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength.

## Can a charged particle change its direction of motion in a magnetic field?

Yes, a charged particle can change its direction of motion in a magnetic field due to the Lorentz force. This force acts as a centripetal force, causing the particle to move in a circular path. As the magnetic field or velocity of the particle changes, the direction of motion will also change.

## What is the significance of the radius of the charged particle's motion in a magnetic field?

The radius of the charged particle's motion in a magnetic field is determined by the strength of the magnetic field, the velocity of the particle, and the mass of the particle. It can be calculated using the equation r = mv/qB, where m is the mass of the particle. The radius can give important information about the particle's velocity and the strength of the magnetic field it is moving through.

Replies
7
Views
3K
Replies
1
Views
994
Replies
13
Views
2K
• Electromagnetism
Replies
14
Views
2K
• Electromagnetism
Replies
1
Views
1K
Replies
8
Views
1K
• Other Physics Topics
Replies
11
Views
696
• Introductory Physics Homework Help
Replies
31
Views
1K