``QUICKIES''   [30 marks -- 5 each]

1.

If $\vec{\mbox{\boldmath$g$\unboldmath }}$ is the acceleration of a small test mass due to the gravitational attraction of a large accumulation of other mass, we can write GAUSS' LAW FOR GRAVITY in the form ${\displaystyle \int\!\!\!\!\int\!\!\!\!\!\!\!\bigcirc\vec{\mbox{\boldmath$g$\un... ...vec{\mbox{\boldmath$A$\unboldmath }} = k{\scriptscriptstyle G} M_{\rm encl} }$, where $M_{\rm encl}$ is the total mass inside the closed surface over which $\vec{\mbox{\boldmath$g$\unboldmath }} \cdot d\vec{\mbox{\boldmath$A$\unboldmath }}$ is integrated. What is the value of the constant $k{\scriptscriptstyle G}$?

2.

A velocity selector has a magnetic field $\vec{\mbox{\boldmath$B$\unboldmath }}$ perpendicular to an electric field of 20,000 V/m. We find that charged particles with velocity $v = 4.0 \times 10^4$ m/s perpendicular to both $\vec{\mbox{\boldmath$E$\unboldmath }}$ and $\vec{\mbox{\boldmath$B$\unboldmath }}$ pass through the device undeflected. What is the strength of $\vec{\mbox{\boldmath$B$\unboldmath }}$ [in Tesla]?

3.

If $\epsilon_\circ$ and $\mu_\circ$ are respectively the permittivity and the permeability of free space, what is the value [including units] of the quantity $(\mu_\circ \epsilon_\circ)^{-1/2}$ and what does it represent?

4.

An electric dipole, consisting of a 0.01 C positive electric charge 1 cm away from an equal-magnitude negative charge, is located at the centre of a sphere of radius 1 m. What is the average value of the dipole's electric field normal to the sphere's surface? Explain.

5.

An oscillator consisting of a coil, a capacitor and a 1000 $\Omega$ resistor, all connected in series, has a resonant frequency of $f_\circ = (1/2\pi)$ kHz and a decay time of $\tau = 0.1$ s. What is the inductance L of the coil?

6.

What is the total relativistic energy of

(a)

an electron with a kinetic energy K_e = 0.511 MeV? E_e =  MeV.
 

(b)

a photon with a momentum of $p_\gamma = 0.511$ MeV/c? $E_\gamma =$  MeV.