Question

(a) (4 marks) Two long, parallel, straight wires spaced d = 0.06 m apart carry currents 4 A and 7 A in opposite directions. Copy the diagram at right showing the two wires and indicating the direction of the currents in each. (i) Draw a vector indicating the direction of the magnetic field caused by the first wire at the position of the second wire. (ii) Indicate the direction of the force experienced by the second wire due to this magnetic field. (iii) Calculate the magnitude of the force (per unit length L) between the two wires. (b) (6 marks) A charged particle in a vacuum chamber moves with constant horizontal velocity at right angles to a uniform horizontal magnetic field of strength B = 4.9x10- T (see figure at right). The particle's speed is y = 2.1 mm sł. The force on the particle due to the magnetic field exactly balances the force due to gravity. 0 O O 0 O 0 0 B 0 o (i) Is the particle positively or negatively charged? Explain your reasoning. (ii) The magnitude of the particle's charge is 5.0x10-'C. What is its mass? (c) (4 marks) A current loop like the one in the diagram on the right is threaded by a uniform magnetic field Bdrive. The magnitude of Bdrive is increased over a short time, causing the magnetic flux through the loop to change. Conducting loop Bdrive Copy the diagram and illustrate the following: (i) A vector AB drive indicating the increase in Bdrive, (ii) A vector indicating the induced magnetic field Binduced (iii) The direction of the induced current linduced in the loop according to Lenz's Law. (d) (6 marks) In the figure at right, a single-loop coil (N-1) of radius Il Coil 2.0 cm and resistance R = 6.0 12 is placed inside a long OOOOOOoooooOOOOOOOOO solenoid with n = 220 turns per cm. The current in the solenoid drops from 1.5 A to zero in a time interval At = 25 ms. মামামামামামামামামামামামামামামামামামাম) Solenoid (i) Use Faraday's Law to derive an expression for the emf induced in the coil. (ii) Calculate the magnitude of the induced emf in the coil. (iii) Use Ohms law to calculate the induced current in the coil.

Answer 1

Solution I 7 Figo ee, I Given that : Il = 4 A I2 = 17A d = 0.06m The magnetic field caused by first wire (I) at the position of the second wire is directed into the page . This field is denoted by Bl. (11) The direction of the tone experienced by the second wise due to Bl is shown in Fig . Both wise will repel each other. due to diffesent direction of curent I & I The magnitude of the fon (per unit tength L) between wire is given as en as 11) f - Mo. Il 22 27 d

t = 2x107x 4 x 7 sid 4 A I2 = 7A 0.06m 21 - o = 2x10 7 NB A2 - - f- 568 107 f = 0.06 >> f 9.33 x16 Newton/mi The fare per unit fength is 9.33 X 105 N/m 0 0 0 0 OR 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g Griven that: B-4.9x105T{ pointed out? ve 2.1 mm Is - 2.1 x 103 mis {.. Imm2103mg The force on particle due to the magnetic field exactly balances the fore due gravity [img = q VB - Both directed in opposite direction

(given that) in ng is directed downwards Therefese magnetic force is directed upwards direction The magnetic force is directed in upwards direction in the plane of paper & the magnetic field is pointed out perpendi to plane of paper. How By Right hand palm nile this is only possible the particle is negatively charged & Direction of speed is opposite to direction of current } (velocity particle is Negatively charged. - CCCCCIIIIIIULULLLLLL Given q = 5.0 X1019 C from egn How ing=q UB JUB m. 3 kg > m=s n. 5.0x1019 X 2.1x 103 x 4.9x105 9.81 m = S. 245 x 1027 kg s. 295 X 10 27 kg The mass of particle is