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Transcript
E & B Fields 28 TH FEBRUARY β BG GROUP What is a field? A field is a physical quantity that has a value for each point in space and time. For example, temperature at the surface of the Earth is a scalar field, it has a single value at every point on the Earth. Wind measurements give a vector field, each point has both a magnitude (wind speed) and direction. What is a field? We represent vector fields using field lines. The lines themselves tell us about the direction of the field. The spacing of the lines tell us the strength of the field; the closer together the lines are, the stronger the field is at that point. Electric field strength Electric field strength is defined as the force per unit charge. πΈ= πΉ π πΈ is the electric field (NC-1) πΉ is the force (N) π is the charge Radial electric fields The field around a point charge is radial, so the force the charge would experience depends on π 2 . Coulombs law allows us to work out the force of attraction or repulsion between two point charges. πΉ= q π1 π2 4ππ0 π 2 πΉ is the force (N) π is the charge (C) π is the separation between the charges (m) π0 is the permittivity of free space Lines of equipotential Radial electric fields The electric field strength at a distance from a point charge is given by: πΈ= π 4ππ0 π 2 πΈ is the electric field strength (NC-1) π is the charge (C) π is the separation between the charges (m) π0 is the permittivity of free space q Lines of equipotential Radial electric fields The distance between two point charges of +8.0nC and +2.0nC is 60mm. At a point between them, the resultant electric field strength Is zero. How far is this point from the +8.0nC charge? +8.0nC +2.0nC q q 60mm Uniform electric fields A uniform field can be produced between two metal plates by connecting them to a cell. 300V The field strength is the same at all points between the plates and is given by: πΈ= π π πΈ is the electric field strength (Vm-1) π is the potential difference (V) π is the separation of the plates (m). 0V Lines of equipotential Charges in electric fields Charged particles move through electric fields like projectiles. The particle will experience a force parallel to the field lines and accelerate in this direction at a constant rate. The path is a parabola. 1000V v = 2×106 ms-1 p 0.1m s 0V 0.2m Calculate the deflection of the proton, s. Electric potential Electrical potential, π, is the electrical potential energy per unit charge and is measured in Volts. π= V π 4ππ0 π To move a charge from one potential to another requires doing work, Ξπ. Ξπ = πΞπ π is positive when the force is repulsive and negative when the force is attractive. Gradient is the field strength Repulsive r V Attractive r Gradient is the field strength Magnetic fields A magnetic field is a region in which a force is exerted on a magnetic material. A current flowing in a wire will produce a magnetic field. The direction of this field can be found using the right-hand rule. Force on a current Motion Field A wire carrying a current in a magnetic field will experience a force. Fleming's left hand rule can determine which direction this force will be in and the magnitude of this force can be determined by: πΉ = π΅πΌπ Current First finger β Field Second finger β Current Thumb β Motion (force) πΉ is the force (N) π΅ is the magnetic flux density (T) πΌ is the current (A) π is the length of wire in the field Force on a current In the situation shown, work out the direction in which the wire will move, and calculate the force exerted on the wire. π΅ = 0.25T 0.1m πΌ = 3A Force on a current The Force is the greatest when the wire and the field are perpendicular. π If π = 90°, πΉ = π΅πΌπ If π = 30°, πΉ = π΅πΌπ × 0.5 If π = 0°, πΉ = 0 For a wire at angle π to the field, the force acting on it is: πΉ = π΅πΌπ sin π. Charges in magnetic fields π£ = 2×106 ms-1 Forces act on charged particles in a magnetic field. This force is given by: πΉ = π΅ππ£ According to Flemingβs left hand rule, the force is always perpendicular to the direction of travel β this results in circular motion. The force is equal to the centripetal force, given by: ππ£ 2 πΉ= π p π΅ = 0.20 T × × × × × × × × × × × × Calculate the radius of curvature, r. Flux, flux density & flux linkage Magnetic flux Magnetic flux density Magnetic flux linkage Symbol: π Symbol: π΅ Symbol: Ξ¦ Unit: Wb (Weber) Unit: T (Tesla) Unit: Wb (Weber) Think of it as the total number of field lines The number of field lines per square meter Total number of field lines within a coil multiplied by the number of turns The descriptions above lead us to the following relationships: π = π΅π΄ Ξ¦ = ππ = π΅π΄π Coil not perpendicular to B If the coil is not perpendicular to the magnetic flux, you can use the following equations to calculate π or Ξ¦. Coil π = π΅π΄ cos π Ξ¦ = π΅π΄π cos π π In each case, π is the acute angle between the normal of the coil and the magnetic flux. Normal to the coil Electromagnetic induction When a conductor moves through a magnetic field, its electrons will experience a force. This means they will accumulate at one end of the conductor inducing an emf just like a battery. An emf is produced when lines of flux are βcutβ, but a current will only be induced if the circuit is complete. × × × × × × × × × × × × Positive charge Negative charge Faradayβs law The induced emf (π) is directly proportional to the rate of change of flux linkage. flux change ΞΞ¦ ΞΞ¦ π= = =π time taken Ξπ‘ Ξπ‘ Ξ¦ π Gradient = π Area = Ξ¦ time time Faradayβs law An aeroplane with a wingspan of 45m is travelling at 950km/h perpendicular to the magnetic field of the Earth. The magnetic field strength is 5×10-5 T. Calculate the emf induced across the wingtips. × × × × × × × × × × × × × × × × × × × × × × × × 45m 264m Finally, use π = π΅π΄ and π = π Ξπ Ξπ‘ to calculate the emf Lenzβs law The direction of the induced emf is given by Lenzβs law. It states that the induced e.m.f is always in such as a direction as to oppose the change that caused it. You can work out the direction of the emf by using Flemingβs left hand rule β with your right hand. π£ = 0.2ms-1 0.1m 0.3m π΅ = 0.25T Calculate the flux cut by the wire, and the emf generated. Flux linkage, emf and phase Ξ¦ / Wb For a rotating coil, flux linkage and induced voltage are 90° out of phase. Flux linkage is given by Ξ¦ = π΅π΄π cos ππ‘ and induced emf can be found with π = π΅π΄ππ sin ππ‘ where π = 2ππ. t/s N π/V S t/s Transformers An alternating voltage in the primary coil produces an alternating magnetic flux. The flux travels through the iron core and induces an alternating voltage in the secondary coil. For an ideal transformer: ππ ππ Is = = ππ ππ Ip For a real transformer: efficiency = ππ πΌπ ππ πΌπ Primary 1200 turns 0.25A 240V Secondary 500 turns Efficiency 83% Calculate the current in the secondary coil Velocity selector A proton is accelerated through a 16kV potential before entering a velocity selector. The velocity selector consists of two parallel plates with a potential difference of 62kV and a separation of 0.2m. Calculate the magnetic field such that the proton is not deflected. 16kV 62kV 0V × × × × × × p 0.2m × × × × × × 0V
