A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50 2. A magnetic field perpendicular to the coil is B (t) = 0.020t +0.010t², where B is in tesla and t is in seconds. (a) Find an expression for the induced current I(t) as a function of time. (b) Evaluate I at t = 5s and t = 10 s.
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- A solenoid has the following dimensions. inner diameter d = 4.22 cm length L = 42.7 cm When a current flows through the coil of the solenoid, the magnetic field inside the solenoid is 5.40 T. (a) Determine the magnetic energy density (in J/m³) in the field. UB = 1.16 Apply the equation for the magnetic energy density and insert values. J/m³ (b) Determine the energy (in kJ) stored in the magnetic field within the solenoid. KJ UB =A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B =50e-0.2tT. What is the magnitude of the current induced in the coil at the time t = 2.0 s? Answer: 2.6 mAA conducting ring of electrical resistance R = 4.0 [2] and radius r = 2.0 [m] is inside an external magnetic field B=6t (T), where t is measured in seconds and whose direction is towards the inside of the page as shown in the figure. What is the magnitude of the induced current for t>0? Express your answer in Amperes and with 2 decimal places of precision. X X X X X X X X X ххххх X X ring
- A 280-turn rectangular coil with area, A = 0.22 m², and resistance, R = 772, is rotating at a constant rate of 66 rpm in a uniform magnetic field, B = 0.473 T. (a) What is the angular speed of the rotating coil? w = 6.908 (b) Calculate the frequency, f, and period, T, of the coil's rotation. f = 1.1 Emax Emin = Induced EMF (2 of 2) (c) Find the maximum, minimum and rms-average emf induced during each rotation. Erms II 6.91 rads/s max Pavg 1.1 Hz and T = 0.909 = V V V (d) Calculate the maximum and average power generated during each cycle. P₁ 0.909 sec W WFor a physics lab assignment, a student needs to create a solenoid using copper wire with diameter d = 0.500 mm. The resistance of the solenoid needs to be 3.50 and the magnetic field of the solenoid with a current of 2.90 A should be 5.90 × 10-² T. Assume the resistance does not change significantly with temperature, and the radius of the solenoid is 1.00 cm. (Use p 1.70 x 10-8.m for the resistivity of copper.) (a) How many turns of wire does the student need? turns (b) Determine the required length (in cm) of the solenoid. cmAt the instant a current of 0.90 A is flowing through a coil of wire, the energy stored in its magnetic field is 4.0 x 10 J. What is the self-inductance of the coil (in H)?
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