Electrons and Ions in Magnetic Fields

2 An electron is situated between two plates 20 mm apart having a p.d. of
600 V. Calculate the force on the electron and its initial acceleration in the field, showing the force in a diagram. Is the electron weight negligible?

4.8 x10^-15 N , 5.4 x10¹⁵ ms^-2  weight e ~ 9 x 10^-30 N

3 The force on a charge of 4e between two plates 32mm apart is 8 x 10^-14 N. Calculate the p.d. V between the plates.  4000V

4 An electron beam with a velocity of 10⁶ ms^-1 enters a magnetic field B of 4 x 10^-5 T everywhere normal to the beam. Calculate the radius of the path PQ of the beam. Explain why PQ is curved downwards.

0.14m

6 In an electron tube, electrons from the cathode C start from rest and move to the anode A through a p.d. of 150 V. Calculate the velocity of the electrons on reaching the anode. 7.3 x10⁶ ms^-1
If the electron beam passes through a hole in the anode, and enters a magnetic field of 10^-4 T normal to the direction of the beam, calculate the radius of the circular path XY in the field. 0.41m

9 An electron beam is accelerated by a p.d. of 300 V, and then enters normally a magnetic field of 10^-3 T. Calculate the velocity reached by the electrons and the radius of its path in the magnetic field. 10⁷ ms^-1 5.8 x10² m

11 An electron beam X moves with velocity v towards two horizontal plates A, D which are 10mm apart. When the pd between A and D is 160V and the electric field force is opposed by a uniform magnetic field B of 2mT, the electrons pass straight though the plates undeflected. Find v and draw a sketch showing the field directions. 8 x10⁶ ms^-1

If the electron beam travels in a circular path of 23mm in the B field alone estimate the charge mass ratio (e/m_e) of an electron. 1.7 x10¹¹ Ckg^-1

Electricity Prep

 

Electric Motor Effect Prep markscheme

 

Y13 Gravity answers

Orbital Speeds

 

 Orbital Speeds                                    r_e = 6371 km

 

1.    Geostationary satellites are used for telecommunications. They appear not to move in the sky. However they do orbit the Earth with a period of 1 sidereal day. (23 hours 56m). There are two other conditions for the satellite to remain above one point on Earth. Over the equator, East à West,

Geostationary satellites orbit the earth at an altitude of 35 786km. Calculate their speed.

T = (23 x 60) + 56 min) = 1436 min x 60 sec =86160 s

r = height + r_e = 6371 +35786= 42157 x1000 m = 4.22 x10⁷m

 = (2 x 3.142 x 4.22 x10⁷) / 86160 = 3074 ms^-1

Similar satellites orbit Mars at an altitude of 17 031 km.  The length of a Martian day is similar to that of the Earth, why are the altitudes so different? .

Mars has less mass than the Earth

Calculate the speed of an Arestationary satellite. T_m = 88642.66 r_m = 3396.2 km. 1448 ms^-1

 

2.    GPS satellites orbit at a height of 20 200km. Their orbital period is 11h 58min earth time (– their time is about 20 microseconds faster due to the relativistic effects of their motion and the Earth’s mass bending space-time). Calculate their orbital speed. 3900 ms^-1

 

3.    NASA’s Mercury messenger probe orbited the planet at an altitude of 201 km, (r_m = 2.44 x 10⁶m) with a period of 5.75 x 10³ s Calculate its speed. 2900 ms^-1

 

 

 

4.    Complete this table

	Distance from Sun (106 km)	Orbital Period (days)	T (Years)	Orbital Speed m/s
MERCURY	57.9	88	0.241096	48 000
VENUS	108.2	224.7	0.615616	35 000
EARTH	149.6	365.2	1.000548	30 000
MARS	227.9	687	1.882192	24 000
JUPITER	778.6	4331	11.86575	13 000
SATURN	1433.5	10747	29.44384	9700
URANUS	2872.5	30589	83.80548	6800
NEPTUNE	4495.1	59800	163.8356	5500
PLUTO	5870	90588	248.1863	4700

 

5.    There are 5 planets orbiting the star tau Ceti (12 light years away and similar to our sun although it’s slightly cooler, 5344K compared to 5778K ) The planets are called a,b,c,d e&f.

Tau Cati F orbits at 1.35 AU from the star. (1AU = 150 million km) with a period of 1.76yrs. Calculate its orbital speed. 22 000 ms^-1

(Assuming that Tau Ceti f is a terrestrial planet, it would likely be at least 2.3 times larger in size than the Earth. With an Earth-like atmosphere, the surface temperature would be approximately −40°C (233 K). With a denser atmosphere able to produce a stronger greenhouse effect it could have a much higher temperature, between 0°C and 50°C, enough for complex life to exist.)

Paying for electricity

1.   21.6p            18.1p

2.   £1.16

3.   0.54kWh

4.   0.42 kWh       0.112p + 3.79p = 3.9p

5.   4.46p            9.34p

Prep on Planet Odyssey

 

(a)     arrow towards centre of planet                                                                                      1

(b)     (i)      g = GM/R2 (Do not allow r)                                                                       1

(ii)     gS/gO = R2/25R2; gS = 40/25 (= 1.6 N kg–1)                                               2

(iii)     gC/gO = R2/16R2 giving gS = 40/16 (= 2.5 N kg–1)                                     1

 

Inverse Square Law

 

Gravitational Fields Prep

 

Radius and density ratios earth moon

F=BILsin theta

1.       A vertical wire carrying a current of 5A is situated in a uniform horizontal magnetic field of 4x10^-3 T. Calculate the magnitude of the force on the wire if the length of the wire in the field is 0.4m. Draw a sketch showing the direction of the force on the wire when the current flows (i) upwards and (ii) downwards.   8x10^-3N

2.       Calculate the force on a wire of length 0.1 m carrying a current of 10A if it is (i) perpendicular, (ii) inclined at 30⁰ (iii) parallel to a field of 1 x10-2 T  0.01N, 0.005N, 0N.

3.       The diagram shows a simple current balance. The loop is balanced when no current flows, and no masses are added. The straight part of the wire is 15cm long and is crossed by a magnetic field of 2.0 x10^-3 T. The current in the wire is 1.0 A. What mass must be hung from the other side in order for the system to balance? g=9.81 ms^-2

31mg

4.       A metal wire 10m long lies east west on a wooden table. What pd would have to applied to the ends of the wire, and in what direction, in order to make the wire rise from the surface. Assume that the electrical connections to wire cause no appreciable constraint.

(density of the metal = 1.0 x 10⁴ kgm^-3, resistivity of the metal = 2 x 10^-8 Ωm, horizontal component of the earth’s magnetic field = 1.8 x 10^-5 T, g = 9.81 Nkg^-1) 1.1kV WàE

LDR as a lightmeter