H216 Electromagnetism-Tutorial (wSolutions)(1718).student

Topic 16: Electromagnetism Page 1 9749 H2 Physics Tutorial Solution Electromagnetism Tutorial Solution Discussion Magnetic field lines D1 (a) The figure illustrates the patterns of the magnetic flux due to a current in a solenoid. (i) On the figure, draw arrows to show the direction of the magnetic field in th e solenoid. [1] (ii) The coils of wire on an electromagnet are usually wound on a ferrous core. State two properties of the core which are important in its use in an electromagnet. [2] It can be easily magnetized / de-magentised, when the current is switched on/off. It concentrates the magnetic field lines and thereby increasing the magnetic flux density at the centre of the coil. (b) A loosely-coiled spring is suspended from a fixed point as illustrated on the right. Electrical connections are made to the ends of the spring. When a current is switched on in the spring, there is a small change in the length of the spring. flexible lead (i) Magnetic field lines

Topic 16: Electromagnetism Page 2 9749 H2 Physics Tutorial Solution (i) On the figure, indicate the direction of the current in the individual turns of the spring and the direction of the magnetic field. [2] (ii) On the figure on the right, draw the pattern of the magnetic field due to a straight current - carrying wire. [1] For this question, check to ensure that the circles they draw are further and further apart. The magnetic flux density should become weaker (field lines further apart) as the distance from the wire increases. Also, it’s a 3D plane, the shape of the field line is an ellipse.

Topic 16: Electromagnetism Page 3 9749 H2 Physics Tutorial Solution D2. X and Y are two coaxial circular coils lying on a table. O, P and Q are three points on the table. Initially, there is a constant current in coil X and no current in coil Y. A small current is now passed through coil Y, which decreases the magnitude of the magnetic flux density at O. How does the magnitude of the flux density changes at P and Q? P Q A Decreases Decreases B Decreases Increases C Increases Decreases D increases Increases Solution: Choose an arbitrary current direction in wire X. Draw the magnetic field pattern due to the current in wire X at the positions O, P, Q. Choose an arbitrary current direction in wire Y to get the resultant magnetic field effect in O. D3. Force on a current-carrying conductor in a magnetic field A straight wire of mass 10 g and lengt h 5 cm is suspended from two identical springs which, in turn, form a closed circuit as shown. The total resistance of the circuit is 12 . Each spring is stretched a distance of 0.5 m under the weight of the wire. When a magnetic field is turned on, dire cted out of the page (indicated by the dots), the springs are observed to stretched an additional 3 cm. (a) Draw a free body diagram on the rod [2] (b) Calculate the force constant of each spring [2] (c) Calculate the magnetic flux density. [4] 5 cm 24 V X Y .O .Q .P

Topic 16: Electromagnetism Page 4 9749 H2 Physics Tutorial Solution (a) (b) Using Hook’s Law T = kx 2T = mg kx = mg / 2 k = (mg/2)(1/x) = [(0.01)(9.81)/2] (1/0.5) = 0.0981 Nm-1 (c) V= IR 24 = I (12) I = 2.0 A For equilibrium, sum of forces in the vertical direction must be zero. mg + F - 2T’ =0 F = 2kx’ – mg = 2(0.0981)(0.53) – (0.01)(9.81) = 5.886 x 10-3 = 5.89 x 10-3 N F = BIL 5.886 x 10-3 = B(2)(0.05) B = 0.05886 T = 0.0589 T - mg F T T T: tension acting rod due to spring mg: weight of rod F: magnetic force acting on rod

Topic 16: Electromagnetism Page 5 9749 H2 Physics Tutorial Solution D4. Equilibrium involving magnetic forces Two smooth electrically conducting vertical tracks are joined by a horizontal metal slide of length 40 mm. The slide is supported by a sensitive spring balance and is free to move up and down the tracks in a uniform horizontal magnetic field, B, at right angles to its length as shown. The spring balance, which is calibrated in milli -newton, reads zero when it is hanging vertically and supporting no load. The tracks are connected to a variable power supply which can provide a current in either direction through the circuit. A student passes various currents through the circuit and notes corresponding readings on the spring. The results are shown in the graph above. (a) Determine the mass of the slide [2] (b) Determine the current flowing when the spring balance reads zero, [2] (c) Indicate the direction of the current on the diagram when the spring balance reads zero [1] (d) Draw a free body diagram showing all forces acting on the slide (e) Calculate the value of the magnetic field B. [3] (a) When no current, I = 0, balance reading = 35 mN Spring balance reading = weight of slide = mg m = 35 x 10-3/9.81 = 3.57 x 10-3 kg (b) Extrapolating onto the I-axis, I = - 3.6 A (c) Applying Fleming’s Left Hand Rule. I: current

Topic 16: Electromagnetism Page 6 9749 H2 Physics Tutorial Solution d) At equilibrium, balance reading is zero (magnitude of current, I = 3.6 A ) Weight of slide = Magnetic force acting on slide, F = BIL mg = BIL B = mg/IL = 35x10-3/ (3.6 x 0.040) = 0.24 T D5. A straight horizontal rod X, of mass 50 g and length 0.5 m, is placed in a uniform horizontal magnetic field of 0.2 T perpendicular to X. Calculate the current in X if the force acting on it just balances its weight. Draw a sketch showing the directions of the current, field and force. [3] For equilibrium, sum of forces in that direction must be zero. (Magneticc force, F) - (Weight of rod, W) = 0 where F = BIL and W = mg BIL = mg A I 9.4 5.02.0 81.91050 3     D6. Electric motor A narrow vertical rectangular coil is suspended from the middle of its upper side with its plane parallel to a uniform horizontal magnetic field of 0.020 T. The coil has 10 turn, and the lengths of its vertical and horizontal sides are 0.10 m and 0.050 m respectively. Calculate the torque on the coil when a current of 5.0 A is passed into it. Draw a sketch showing the directions of current, field and torque. [4] FB = NBIL  = FB x d = NBILd = (10)(0.020)(5)(0.10)(0.050) = 5.0 x 10-3 Nm F: magnetic force on wire Weight of rod: mg F: magnetic force on wire Weight of rod: mg I, Current X X X X X X X X X X X X X X X X X X Magnetic field lines into the plane of the paper

Topic 16: Electromagnetism Page 7 9749 H2 Physics Tutorial Solution D7.Current balance A small coil of N turns has sides of length L and is mounted so that it can pivot freely about a horizontal axis PQ, parallel to one pair of sides of the coil, through its centre (see figure). The coil is situated between the poles of a magnet which produces a uniform magnetic field of flux density B. The coil is maintained in a vertical plane by moving a rider of mass M along a horizontal beam attached to the coil. When a current I flows through the coil, equilibrium is restored by placing the rider a distance x along the beam from the coil. (a) Starting from the definition of magnetic flux density, show that B is given by the expression [4] (b) The current is supplied by a battery of constant e.m.f. , E, and negligible internal resistance. (i) Show that the current in the coil is given by the expression Hint: use (ii) Hence, discuss the effect on x if the coil is replaced by one with: (1) sides of length L with 2N turns, (2) N turns with sides of length L/