1# Fields 2 3Non-contact forces: 4- strong nuclear force 5- weak nuclear force 6- electromagnetic force (dipoles) 7- gravitational force (monopoles) 8 9--- 10 11## Gravity 12 13### Newton's law of universal gravitation 14 15$$F_g=G{{m_1m_2}\over r^2}$$ 16 17where 18$F_g$ is the gravitational force between $m_1$ and $m_2$ 19$G$ is the gravitational constant, $6.67\times 10^{-11} \operatorname{N m^2kg^{-2}}$ 20$r$ is the distance between centre of $m_1$ and $m_2$ 21 22 23- inverse square law 24- acceleration can be calculated from $F_g$, since $F=ma$ 25- all objects with mass attract each other with $F_g$ 26- $F_g$ acts equally on $m_1$ and $m_2$ 27- acceleration of an object close to earth's surface can be approximated by ignoring its mass ($m_2 \approx 0$) 28- apparent weight may be different to gravitational (normal) weight 29 30### Gravitational fields 31 32$$g={F_g \over m}=G{M \over r^2}$$ 33 34where 35$g$ is the gravitational field strength 36$F_g$ is the force due to gravity ($=G{{m_1m_2}\over r^2}$) 37$m$ is the mass of object in the field 38$M$ is the mass of the central body 39 40- arrows towards centre of object 41- closer arrows mean larger force 42- parallel field lines - uniform field strength (vector) 43 44Characteristics of gravitational fields: 45- monopoles 46- attractive force 47- extends to infinite distance, but diminishes with inverse square law 48 49### Work in a gravitational field 50 51Gravitational potential energy: $E_g = mg \Delta h$ 52Work: $W = \Delta E_g = Fx$ 53 54Area under force-distance graph = $\Delta E_g$ 55Area under field-distance graph = $\Delta E_g / \operatorname{kg}$ 56 57### Satellites 58 59## Electromagnetism 60 61### Electric fields 62 63- surrounds +ve and -ve charges 64- exerts force on other changes in its field 65- monopoles and dipoles 66- attractive/repulsive forces 67- can be constrained to a fixed distance (conductors / insulators) 68- current flows from +ve to -ve 69 70#### Field lines 71- +ve to -ve 72- start and end $\perp$ to surface 73- field lines never cross 74- point charges - radiate from centre 75 76#### Forces 77 78$$F=qE$$ 79 80where 81$F$ is the force on charged particle 82$q$ is the charge of object experiencing force (Coulombs) 83$E$ is the strength of the electric field (Newtons / Coloumb or Volts / metre) 84 85#### Work in electric fields 86 87$$W=qV$$ 88 89where 90$W$ is the work done on +ve point charge or in field 91$q$ is the charge of point charge being acted on 92$V$ is the potential (voltage) between points 93 94#### Coulomb's law 95 96 97$$F=k{{q_1q_2}\over r^2}$$ 98 99where 100$k$ is Coulomb's constant $9.0\times 10^9 \operatorname{N m^2 C^{-2}}$ 101$q_1$ and $q_2$ are the charges on the interacting points 102 103 104#### Electric field at distance from a charge 105 106$$E=k{Q \over r^2}$$ 107 108### Electromagnetism 109 110#### Lenz's law 111- Right hand grip rule (relationship between directions of $I, F$) 112 113#### Solenoids 114- Coil around core (like a transformer but field is transferred to kinetic energy) 115 116#### Magnetic force on charged particles 117 118$$F=qvB$$ 119 120where 121$v$ is the component of velocity which is $\perp$ to magnetic field 122 123#### Right hand slap rule 124 125 126**Field, current and force are all 90 degree to each other** 127<pre> 128force 129| / field 130| / 131|/ 90 de= 132 \ 133 \ +ve charge 134</pre> 135 136Force is given by $F=nBIl$ 137 138### Motors 139 140#### DC 141 142- current-carrying wire experiences magnetic force $F$ equal to $nBIl$ 143- torque: $\tau = r_{\perp} F$ 144- split ring and brushes