E & B Fields 28 TH FEBRUARY – 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

Radial electric fields q Lines of equipotential

Radial electric fields 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? qq +8.0nC+2.0nC 60mm

Uniform electric fields 300V 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 0V p 0.2m v = 2×10 6 ms m s Calculate the deflection of the proton, s.

Electric potential r V r V Attractive Repulsive Gradient is the field strength 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 First finger – Field Second finger – Current Thumb – Motion (force) Field Motion Current

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. 0.1m

Force on a current The Force is the greatest when the wire and the field are perpendicular.

Charges in magnetic fields ××× × × × × × × ××× p Calculate the radius of curvature, r.

Flux, flux density & flux linkage The descriptions above lead us to the following relationships:

Coil not perpendicular to B Coil 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 ‘cut’, but a current will only be induced if the circuit is complete. ××× × × × × × × ××× Positive charge Negative charge

Faraday’s law time

Faraday’s 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

Lenz’s law The direction of the induced emf is given by Lenz’s 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 Fleming’s left hand rule – with your right hand. 0.3m Calculate the flux cut by the wire, and the emf generated. 0.1m

Flux linkage, emf and phase NS t / s

Transformers 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. 62kV 0V p 0.2m ×× × × × × ×× ×× ×× 16kV 0V