Question

3. a) Describe Ampere's Law for a long straight wire carrying a current, and Faraday's (5 marks) b) A circular loop of area 0.10m2, is perpendicular to a unifom magnetic field, B. The Law of induction, and Lenz's Rule for a loop of wire in a magnetic field. loop contains a resistor (i) What is the EMF across the resistor where the magnitude of the magnetic field varies with time according to B = 0.10-0.04t, with B in teslas and tin seconds? In a diagram, show the directions of the magnetic field and the (3 marks) (ii) What is the maximum EMF across the resistor, where the magnetic field is instead held constant at B 0.10 T, and the loop rotates about an axis resultant current in the loop. perpendicular to the magnetic field at a steady 0.20 rotations per second? (2 marks)

Answer 1

3 (a) Ampere's law for a long straight wire carrying a current: It states that as, J B.ds- Ho lenc B cos θ ds-10 ienc B.ds o lenc where, B magnetic field measured in T Ho permeability of free space 4Tx 107 mT/A ienc - current enclosed by loop measured in A Faraday's law of induction: It states that an instantaneous emf induced in a circuit which equals to the rate of change of magnetic flux through a circuit. Michael Faraday made fundamental discoveries in magnetism, electricity and light. Mathematically, we have N(d dt) where, N = number of turns magnetic flux measured in Tm2 t - time measured in sec

Lenz's Rule : It state that the polarity of an induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through a circuit. b. A circular loop of area is perpendicular to a uniform magnetic field, The loop contains a resistor. (i) The EMF across the resistor which will be given by using a formula, we have EMF =-A (dB/ dt) EMF =-A {d [(0.1 )-(0.04) t] dt} EMF= (0.1 m2) (0.04 T/s) EMF 0.004 V EMF 4 mV (ii) The maximum EMF across the resistor will be given by using a formula, we have EMFmax-B A w sin θ where, B magnetic field 0.1 T A- area of circular loop 0.1 m2 w = angular velocity = 0.2 rot/sec = 1.2566 rad/s then, we get EMFmax [(0.1 T) (0.1 m2) (1.2566 rad/s)] sin 90 EMFmax 0.012566 V EMFmax12.5 mV