Applications of Magnetic Fields

[stonecoldgen]

Homework Statement

An ion with a charge of +1e enters a region where the electric field produced by parallel plates at 630V separated by 7.0mm is at right angles ot a magnetic field B=450mT. The ion moves a straight line. Find the magnitude of the electric field and the speed of the ion.

Homework Equations

F=qvB
Ampere's Law B=μ₀I/2∏r

The Attempt at a Solution

Is this a mass spectrometer?

first of all, because the plates are parellel the force is maximized (sin90=1)

I am confused, isn't the ion supposed to curve in a radius defined by: r=mv/qB (mv²/r=qvB)

I just don't know what to do since the ion doesn't curve.

Thanks.

 

[gneill]

Homework Statement

An ion with a charge of +1e enters a region where the electric field produced by parallel plates at 630V separated by 7.0mm is at right angles ot a magnetic field B=450mT. The ion moves a straight line. Find the magnitude of the electric field and the speed of the ion.

Homework Equations

F=qvB
Ampere's Law B=μ₀I/2∏r

The Attempt at a Solution

Is this a mass spectrometer?

first of all, because the plates are parellel the force is maximized (sin90=1)

I am confused, isn't the ion supposed to curve in a radius defined by: r=mv/qB (mv²/r=qvB)

I just don't know what to do since the ion doesn't curve.

Thanks.

A moving charge in a magnetic field curves because the Lorentz force acts as a centripetal force. In this case the fields are arranged in such a way that the electric force cancels the magnetic force, so the path never bends. But since the force on the moving charge depends upon its velocity, this cancellation will occur only for same-charge particles with a specific velocity.

It's not a mass spectrometer; it behaves as a velocity selector.

 

[stonecoldgen]

sorry, can you please tell me how to work with velocity selectors? thanks I really appreciate it

 

[gneill]

sorry, can you please tell me how to work with velocity selectors? thanks I really appreciate it

Look up the Lorentz Force. It's comprised of the sum of the forces on charge due to electric and magnetic fields. In this problem you're told that the particle moves in a straight line at some velocity v, so what's the net force?

 

[asteriatic]

I would like to clarify that the ion's trajectory will not necessarily be a straight line even though it is not curving. This is because the electric and magnetic fields are acting on the ion simultaneously, resulting in a combination of forces that will affect its path.

To solve for the magnitude of the electric field, we can use the equation F=qE, where F is the force exerted on the ion, q is its charge, and E is the electric field. We can rearrange this equation to solve for E: E=F/q.

Using the given information, we know that the force on the ion is qvB, where v is its speed and B is the magnetic field. Plugging this into the equation for E, we get E=(qvB)/q. The q's will cancel out, leaving us with E=vB.

To find the speed of the ion, we can use the equation F=qvB and rearrange it to solve for v: v=F/qB. Plugging in the given values, we get v=(qvB)/qB. The qB's will cancel out, leaving us with v=F/B.

We can now plug in the values for F and B to find the speed of the ion: v=(1e)(450mT)/1.602x10^-19C. This gives us a speed of approximately 2.8x10^6 m/s.

In conclusion, the magnitude of the electric field is equal to the product of the ion's speed and the magnetic field, and the ion's speed can be calculated using the force exerted by the electric and magnetic fields. This type of experiment could potentially be used in a mass spectrometer, but more information would be needed to confirm that.