Irodov – Problems in General Physics

3.218. The gas between the capacitor plates separated by a dist-

ance d is uniformly ionized by ultraviolet radiation so that ni elect-

rons per unit volume per second are formed. These electrons moving

in the electric field of the capacitor ionize gas molecules, each electron

producing cc new electrons (and ions) per unit length of its path.

Neglecting the ionization by ions, find the electronic current den-

sity at the plate possessing a higher potential.

3.5. Constant Magnetic Field. Magnetics

• Magnetic field of a point charge q moving with non-relativistic
  locity v:

B

q [yr]

ve-

(3.5a)

(3.5b)

(3.5c)

(3.5d)

(3.5e)

— (^) r 3

• Biot-Savart law:
  I [dl , r]

dB= 111° 4:t Uri (^) r 3 dV, dB= 431 r3 •

• Circulation of a vector B and Gauss's theorem for it:

dr = μo /, §B dS = 0.

• Lorentz force:
  F = qE q [vB].


• Ampere force:
  dF = [jB] dV, dF = I [dl, B].


• Force and moment of forces acting on a magnetic dipole pm = I S n:

F=pm OB, N-- [pmB], (3.5f)

where OBIOn is the derivative of a vector B with respect to the dipole direction.

• Circulation of magnetization J:

(),J dr = I', (3.5g)

where I' is the total molecular current.

• Vector H and its circulation:

H=

— J, H dr = /, (3.5h)

where I is the algebraic sum of macroscopic currents.

• Relations at the boundary between two magnetics:
  B2n, H = H2i• (3.5i)


• For the case of magnetics in which J = xH:
  B = μp,^0 11, μ = 1^ x.^ ( 3. 5 j)

3.219. A current I = 1.00 A circulates in a round thin-wire loop
of radius R = 100 mm. Find the magnetic induction
(a) at the centre of the loop;