Ex30 A circular loop of surface S=20cm² is placed in a homogeneous magnetic field B varying periodically at the frequency of 50Hz as B(t) = a *t or a =5 T/s. The loop is made of a copper wire with a diameter of 5mm. (a) graph the induced voltage Uind (t) and the induced current lind(t). B(t) www.
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- Problem 10: A magnetic needle with magnetic moment μ-0.065 Am2 is placed in a uniform magnetic field B0.65 T as shown in the figure. The angle between the direction of the magnetic moment and the direction of the magnetic field is θ 250 Randomized Variables μ= 0.065 Arn B- 0.65T θ 250 Δ Part (a) Express the potential energy U in terms oft, B, θ. | cos(p) sin(p) | cos(α) sin(a) cos(0) sin(0) ( HOMI 4 5 6 BACKSPACE CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback. Part (b) Calculate the numerical value of U in J. Part (c) If θ can be changed, which value has the minimum potential energy? Part (d) If θ can be changed, which value has the maximum potential energy in degrees? Δ Part (e) Ignore the mass of the needle, express the work needed to change the angle from θ to α in terms oftı, B, θ, α Part (f) If α-1500, calculate the numerical value of the work in J.29.22 A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ohms is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of dB/dt = −0.680 T/s. (a) Is the induced current in the loop clockwise or counterclockwise? (b) What is the rate at which electrical energy is being dissipated by the resistance of the loop?Consider two thin wires of length w with a uniform current I as shown in figure below. Determine the magnetic flux density B(F) at the point P(w,w,0). Show the direction of the magnetic flux density at the given point. W I Z W P(w,w,0) y
- The Hall effect can be used to determine the density of mobile electrons in a conductor. A thin strip of the material being investigated is immersed in a magnetic field and oriented so that its surface is perpendicular to the field. In a particular measurement, the magnetic field strength was 0.735 T, the strip was 0.101 mm thick, the current along the strip was 2.95 A, and the Hall voltage between the strip's edges was 2.95 mV. Find the density n of mobile electrons in the material. The elementary charge is 1.602 x 10-19 C. 1.56 x104 n 3= -3 IncorrectAn electrically conductive rod is moving through a uniform magnetic flux at a constant velocity at right angles, as shown by its cross-section in the diagram. The velocity is in the x-direction, the rod is of length 150 mm along z, and the magnetic flux density is 0.2 T in the positive y-direction. Speed If the potential difference (voltage) across the ends of the rod is 5.8 Volts, what is the magnitude of the velocity? m/s Not perpendicular If the rod is passing through the flux with its axis not at right angles what can you be sure of? The speed to generate 5.8 V would have to be smaller. • The speed to generate 5.8 V would have to be bigger. The speed to generate 5.8 V would be the same.A cube of edge length = 5.00 cm is positioned as shown in the figure below. A uniform magnetic field given by B = (4.9 î+ 4.0 ĵ + 3.0 k) T exists throughout the region. y l B (a) Calculate the magnetic flux through the shaded face. mWb (b) What is the total flux through the six faces? mWb
- A cube of edge length = 4.60 cm is positioned as shown in the figure below. A uniform magnetic field given by B = (6.5 î+ 4.0 ĵ + 3.0 k) T exists throughout the region. B # i (a) Calculate the magnetic flux through the shaded face. mWb (b) What is the total flux through the six faces? mWbThe conducting loop of the shape shown in the figure is being pulled out of a constantBext magnetic field at a constant speed v. The left part of the loop KN is a semicircle ofradius a. The top and the bottom parts of the loop are equal, KL=NM=b. Theresistance per unit length of the conductor is r (Ω/m). During the time intervalbetween when line LM and then KN are at the border of the magnetic field,a) What is the direction ofthe induced current? Explainyour choice of direction.b) What is the EMFproduced in the loop?c) What is the size of theinduced current?A square wire with side a = 0.085 m is in a time-varying magnetic field with magnitude B(t) = At, where A = 0.15 T/s. The plane in which the square is located has an angle θ with the direction of B. Express the magnitude of the magnetic flux going through the loop, Φ, in terms of A, t, a and θ. a. Express the derivative of the flux with respect of time, dΦ/dt. b. Express the magnitude of the emf induced in the loop, ε, in terms of A, a, and θ. c. Calculate the numerical value of ε when θ = 0, in volts. d. Calculate the numerical value of ε when θ = 90°, in volts.