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6/8/23, 6:20 PM The Expert TA | Human-like Grading, Automated! [23 Summer I] PHYS270 5 Faraday's Law magnetic field with magnitude B. As shown in the figure, the field direction is perpendicular to the plane of the loop. The magnitude of the magnetic field changes ata 4 constant rate from B; =0.85 T to By =2.5 T in time At =4.5 s. The resistance of the wire is R =17 (. | —— | f,--""" L B | JRF—‘“"’” Problem 1: A loop of wire with radius r =0.045 m is placed in a region of uniform A + Part (a) Calculate, in Tesla squared meters, the magnitude of the change in the magnetic flux. Numeric : A numeric value is expected and not an expression. AP = T - m? Part (b) Calculate, in volts, the average EMF induced in the loop. Numeric : A numeric value is expected and not an expression. €= V Part (c) Calculate, in amperes, current induced in the loop. Numeric : A numeric value is expected and not an expression. I= A Problem 2: A conducting rod spans a gap of length L = 0.478 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = (.55 T pointing into the paper is in the region. The rod is moving under an external X X X X X X force with an acceleration a = At2, where 4 = 6.5 m/s*. The resistance in the wire is R = B 125 Q. X X X X X X R L vV - Randomized Variables —) X X X X X X L=0.478 m B=0.55T X X X X X X A=6.5m/s? R=125Q 4 v X | ©theexpertta.com Part (a) Express the magnitude of the magnetic flux going through the loop, @, in terms of B, x and L. Expression D = Select from the variables below to write your expression. Note that all variables may not be required. a’ B’ 09 A’ B’ d’ g’ h’ i’ j’ L’ m’ P’ t’ X Part (b) Express the speed of the rod, v, in terms of 4 and ¢. Assume v=0at ¢t =0. Expression v — Select from the variables below to write your expression. Note that all variables may not be required. a’ B’ 0’ A’ B’ d) g’ h’ i) j’ L’ m’ P’ t’ X Part (c) Express the position of the rod, x, in terms of 4 and . Assume x =0 at £ = 0. Expression x = https://ush22md.theexpertta.com/Common/ViewAssignmentDetails.aspx 1/5

6/8/23, 6:20 PM The Expert TA | Human-like Grading, Automated! Select from the variables below to write your expression. Note that all variables may not be required. ,,0,A,B,d, g, h,i,j,L,m, P, t x Part (d) Express the derivative of the magnetic flux, d®/dt, in terms of B, A4, L and ¢. Expression do/dt = Select from the variables below to write your expression. Note that all variables may not be required. a’ B) 09 A’ B) d) g’ h’ i? j? L? m, P) t) X Part (e) Express the magnitude of the emf induced in the loop, ¢, in terms of B, L, A and . Expression 8 = Select from the variables below to write your expression. Note that all variables may not be required. a’ B’ 09 A) B) d) g) h) i? j? L? m? P7 t) X Part (f) Express the current induced in the loop, /, in terms of € and R. Expression I= Select from the variables below to write your expression. Note that all variables may not be required. u’ B’ 89 BSA’BQ d’ g’ h’ i’j’ mDPDRDt Part (g) Express the current induced in the loop, 7, in terms of B, L, A4, ¢, and R. SchematicChoice : BLAt? y BLAt3 . BAt? ~ 3R 3 3R ~ LAt3 , BLAt? BLAt? R R '="3R Part (h) Calculate the numerical value of 7 at # = 2s in A. Numeric : A numeric value is expected and not an expression. I(t=2s) = Problem 3: A flat rectangular wire loop is positioned next to a long straight current-carrying wire. Both the loop and the wire are in the plane of the page, and the direction of the current is clearly indicated in the figure. https://ush22md.theexpertta.com/Common/ViewAssignmentDetails.aspx 2/5

6/8/23, 6:20 PM The Expert TA | Human-like Grading, Automated! Part (e) Due to an external force, the loop begins to move towards the right of the page. Which statement best describes the change in the magnitude of the magnetic flux, |® |, and the direction of any induced EMF, £, as the loop just begins to move? MultipleChoice : 1) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, £, is clockwise around the loop. 2) The magnitude of the magnetic flux, |® 5|, decreases, and the direction of the induced EMF, £, is clockwise around the loop. 3) The magnitude of the magnetic flux, |®p|, decreases, and there is no induced EMF around the loop. 4) The magnitude of the magnetic flux, |® |, is constant, and there is no induced EMF around the loop. 5) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, £, is counterclockwise around the loop. 6) The magnitude of the magnetic flux, |® |, decreases, and the direction of the induced EMF, &, is counterclockwise around the loop. Part (f) The magnitude of the electric current in the long straight wires decreases monotonically towards zero. Which statement best describes the change in the magnitude of the magnetic flux, |® |, and the direction of any induced EMF, £? MultipleChoice : 1) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, &, is clockwise around the loop. 2) The magnitude of the magnetic flux, |®p|, decreases, and the direction of the induced EMF, &, is clockwise around the loop. 3) The magnitude of the magnetic flux, |®p|, decreases, and there is no induced EMF around the loop. 4) The magnitude of the magnetic flux, |® |, is constant, and there is no induced EMF around the loop. 5) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, &, is counterclockwise around the loop. 6) The magnitude of the magnetic flux, |®p|, decreases, and the direction of the induced EMF, &, is counterclockwise around the loop. Part (g) Due to an external force, the loop begins to move towards the bottom of the page. Which statement best describes the change in the magnitude of the magnetic flux, |®p|, and the direction of any induced EMF, £, as the loop just begins to move? MultipleChoice : 1) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, &, is clockwise around the loop. 2) The magnitude of the magnetic flux, |® |, decreases, and the direction of the induced EMF, &, is clockwise around the loop. 3) The magnitude of the magnetic flux, |®p|, decreases, and there is no induced EMF around the loop. 4) The magnitude of the magnetic flux, |® g/, is constant, and there is no induced EMF around the loop. 5) The magnitude of the magnetic flux, |®p|, increases, and the direction of the induced EMF, &, is counterclockwise around the loop. 6) The magnitude of the magnetic flux, |®p|, decreases, and the direction of the induced EMF, £, is counterclockwise around the loop. Problem 4: An oscillating, vertically-oriented magnetic field is given by B(t) = By sin(wt), where By = 0.59 T and w = 8.5 rad/s. Part (a) What is the magnetic flux, in webers, through a horizontal circle of radius 79.25 cm at t = 0? Numeric : A numeric value is expected and not an expression. ®= Wb Part (b) What is the time derivative of the magnetic flux, in webers per second, through this circle at t = 0? Numeric : A numeric value is expected and not an expression. \(\text{d}\Phi/\text{d}t = Whb/s Part (c) What is the magnitude of the electric field, in newtons per coulomb, around the circumference of the circle at t = 0? Numeric : A numeric value is expected and not an expression. E= N/C https://ush22md.theexpertta.com/Common/ViewAssignmentDetails.aspx 4/5

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