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magnetic field

2. Series 24. Year - 1. Warm-Up


  • Jakub's breakfast

Every morning Jakub enjoys his favourite cereals which he pours into a bowl of milk. Assume the bowl is of circulur frustum shape with upper and lower radius $R$ and $r$ respectively ($R$ \geq r$)$, that the cereals are little solid spheres and that before he puts the cereals into the bowl there is milk of height $h$. What is the maximum amount of cereals he can fit into the bowl? You also know that the fraction of volume the cereals occupy inside a fully filled box is $\kappa$.

  • Magnetic monopole

Let's have a metal plate magnetized in such a way that the upper and lower sides are the north and south poles respectively. We use these plates to create two semispheres with the outer side being the north pole. Now, if we glue these two semispheres together, we effectively get a magnetic monopole, which, as we know, can not exist in our world. Where did we go wrong?


5. Series 23. Year - 2. a spring of Lukáš’

Lukáš found an old sofa spring of force constant $k$, coil radius $r$, length $l$ and the number of coils $n$. Since he was bored, he connected the spring to electric current $I$. How did the action change the force constant of the spring?

Lukáš's idea after Aleš told him to have one

2. Series 23. Year - P. telekinesis

Where does permanent magnet take the energy to lift stuff? We know, that magnetic force cannot do any work. Lorenz equation$\vect{F}$ = q ( \vect{v}\times \vect{B})$ says, that magnetic force is perpendicular to the velocity of moving charge and therefore only change its direction.

lámalo hlavu Honzovi Humplíkovi

6. Series 21. Year - E. magnetic lock

[on request you can get a piece of magnet] Measure the dependence of magnetic force between 2 magnets.

Hint: place a piece of paper between magnets and measure the force needed to separate the magnets.

Vyplodil Honza Prachař.

2. Series 21. Year - 4. charged aerial

Two identical charges are at the end of stiff non-conductive rod. What power will be needed to rotate rod at constant angular speed with axis going through the middle of the rod? The friction is negligible

Úlohu vymyslel Martin Výška.

6. Series 19. Year - 3. spinning the electrical motor

On the axle of motor the sting is winded up. At the end of the string a small mass $m$ is fixed. If the motor is connected to the ideal voltage source of voltage $U$, small mass travels up at speed $v_{1}$. What speed will the small mass reach, if the voltage source is disconnected and the motor contacts are connected (shorted)? Assume friction-less devices.

Našel Matouš v sovětské sbírce.

1. Series 19. Year - 4. get a loop


Assume circular loop made from wire. The current is fed by radial wires (see figure). What is the magnetic field in the middle of the loop? The radius of the loop is $R$, the angle between radial wires $φ$ and the current in the wire is $I$.

Navrhl Matouš.

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