Teacher Xu, Please Take Care of the Reckless Students in Your Class

She didn't stop from beginning to end!

But after finishing the work, when she should read the fourth question, she stopped and kept looking at the third question.

Three invigilators, "???"

Qian Mengmeng carefully reviewed the question.

地球赤道表面附近处的重力加速度为g0=9.8m、s^2，磁场的磁感应强度的大小B0=3.0*10^-5T，方向沿经线向北。

The magnitude of the magnetic induction over the equator is inversely proportional to r^3 (r is the distance from the survey point to the center of the earth), and the direction is parallel to the direction of the magnetic field near the equator.

Assuming that at the distance r=5Re from the earth's center above the equator (Re is the radius of the earth), there is a plasma layer with a thickness of 10km consisting of equal numbers of protons and electrons (the magnetic field in the layer can be regarded as a uniform magnetic field), each particle The number density is so low that the interactions of charged particles are negligible.

已知电子的质量me=9.1*10^-31kg，质子的质量mp=1.7*10^-27kg，电子电荷量为-1.6*10^-19C，地球的半径Re=6.4*10^6m。

1. On the one hand, electrons and protons in the plasma layer under investigation make random motions; the current density.

2. Now imagine that all electrons and protons in the plasma layer point to the center of the earth, the initial velocity of electrons is ue= *10^4m/s, and the initial velocity of protons is up=3.4*10^2m/s , try to explain by calculation that these electrons and protons are impossible to reach the surface of the earth.

The three invigilators looked at each other as they watched Qian Mengmeng's reluctance to continue with the following questions.

In the end, they made eye contact and decided that it was Qin Mengmeng checking whether her problem-solving process was wrong!

But the next second-

Qian Mengmeng started writing, her nib did not appear under other topics, it was the third one!

The three invigilators gasped, and at this moment, they finally understood why!

Sure enough, Qian Mengmeng wrote "Solution [-]"!

The reason why she paused is because on this question, she has a different way of solving the problem!

With these three words written out, Qian Mengmeng's hand speed is amazing again!

Since the thickness of the plasma layer is much smaller than the radius of the earth, both the gravitational field and the magnetic field in the investigated plasma region can be regarded as uniform fields.

The magnetic induction intensity of the magnetic field in this region...

……

Investigate a particle in the plasma layer with a mass of m, a charge of q, and an initial velocity of u. Take the location of the particle as the coordinate origin O, and make a rectangular coordinate system Oxyz. The Ox axis points to the center of the earth, and Oz is along the direction of the magnetic field. as the picture shows.

She also made the main animation!

Then continue:

The three components of the initial velocity of the particle in the coordinate system are ux, uy and uz. Since the gravitational force acting on the particle is along the positive direction of the x-axis, the Lorentz force acting on the particle is perpendicular to the z-axis, so the particle is in the z-axis. The axial direction is not affected by the force, and the component velocity along the z-axis remains unchanged.

Now imagine that at the beginning, a velocity of v0 along the positive y-axis is attached to the particle, and a velocity of v0 along the negative y-axis is attached to the particle, and the Lorentz force associated with one of the v0 is required to be exactly the same Balanced with the Earth's gravitational pull on the particles...

……

The three invigilators no longer knew what to say.

People are racing against time to solve the problem, racking their brains to get the answer, but you are lucky, after you get it, you still have time to think about the second problem-solving idea!

Outrageous!

It's outrageous!

Where is the Olympic Physics Screening Test!

It's totally like playing!

The three invigilators gasped, but just when they thought this was enough to defy the sky.

After Qian Mengmeng ended the second problem-solving idea, she still did not turn the page!

Fuck, fuck, fuck!

Qian Mengmeng paused again, which made the three invigilators heartbroken.

Their faces were even pale, and their hearts were roaring: There is no third way to solve the problem!impossible!This is absolutely impossible!

But unfortunately, Qian Mengmeng wrote in the blank space of this question: Solution [-]!

Just when these three hadn't reacted, Qian Mengmeng wrote faster and more.

……

According to the formula (6) vz=uz, it can be known that the magnitude and direction of the particle velocity along the z-axis remain unchanged, but it is different for different particles, and belongs to the velocity component of the random motion of the particles in the plasma layer.

According to the formula (7), vx=Vx, vy=Vy-v0 can be obtained, indicating that the particle moves along the y-axis at the speed of 0v while the particle is moving in a circle at the speed V in the Oxy plane.

Vx, Vy are the x and y components of the circular motion velocity.

The orbital radius of circular motion is not only related to the mass of the particle, but also related to the x component ux and the y component uy of the particle's initial velocity.

The speed direction of circular motion varies with time, and the average speed in one cycle of circular motion is equal to 0.

The velocity v0 along the y-axis is given by the formula (8), and its magnitude is constant, independent of the initial velocity of the particle. The same particle is the same, but for the positively charged particle, its direction is along the negative direction of the y-axis. Negatively charged particles oriented in the positive direction of the y-axis.

It can be seen that although the electrons and protons in the plasma layer are quite complex, each particle has a velocity v8 given by the formula (0), and its direction is perpendicular to the earth's gravitational force where the particle is located. Proton, heading east...

The answer is exactly the same as the above two!

The first question is!