I'll answer the first three questions first, but the latter electromagnetism is a textbook example, which is very simple. I hope the landlord will answer it himself, not just asking for help.

2, dv= 12tdt, bilateral integration, get V = 6t 2+v0, dx=vdt, bilateral integration, get X = 3t 3+v0t+x0.

3. momentum conservation, mu0=(M+m)v, and v=mv0/(M+m) is obtained. W=v/(2L/3) is obtained.

Ek can be integrated. 0.5pdx (wx 2) = de, two-sided integration, p is density, and ek = ml 2 (w 2)/6 is obtained.

4. The basic effect of relativity, r = sqrt (1-(u/c) 2), then m' = m0/r. The direction of motion becomes a' = a * r. And a = v0 (1/3).

Therefore, the moving volume v' = a' * a * a = v0 * R. The moving density p = m'/v' = m0/(v0 * r 2).

Tip:

5. The differential definition of electric field intensity can be used, the internal superposition of electric field is strengthened, and the potential can be integrated by electric field intensity, paying attention to the boundary conditions of integration.

6, c = es/d. After inserting the copper plate, d decreases and c increases. The calculation model, which is equivalent to two capacitors in series, obviously has nothing to do with the position of the copper plate, but only with the thickness. The energy of the capacitor can be calculated directly according to the formula.

7. The integral is directly calculated by Safar formula.

8, the law of electromagnetic induction, b multiplied by cos60, and then directly take the differential. And the induced potential is obtained. Ohm's law is used for the direction of current, and the right hand rule is used.