A 2.44 m long solenoid containing 300 loops is wound on an iron core (magnetic permeability m = 2000 m0) along with a second coil of 100 loops. The loops of each coil have a radius of 2.00 cm. If the current of the first coil drops uniformly from 12.0 A to zero in 98.0 ms, determine (a) the mutual inductance M, and (b) the emf induced in the second coil.
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P1 Please solve this problem very clearly and briefly with step by step explanation.
Question - A 2.44 m long solenoid containing 300 loops is wound on an iron core (magnetic permeability m = 2000 m0) along with a second coil of 100 loops. The loops of each coil have a radius of 2.00 cm. If the current of the first coil drops uniformly from 12.0 A to zero in 98.0 ms, determine (a) the mutual inductance M, and (b) the emf induced in the second coil.
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- The distance between the wire and the circular current loop is r = 2.4 cm. (Figure 1) Figure O 2.0 A -Wire 0.20 A 1 of 1 2.0 mm What is the magnitude of the torque on the circular current loop? Express your answer with the appropriate units. T = Submit Part B μÀ Value Request Answer Units What is the loop's stable equilibrium position? ? O The dipole will be in equilibrium after rotating clockwise 135°. O The dipole will be in equilibrium after rotating clockwise 180°. O The dipole will be in equilibrium after rotating clockwise 45°. O The dipole will be in equilibrium after rotating clockwise 90°.7. Consider two semi-infinite wires connected with a 4 circular bend and current i flowing as shown. Using an appropriate combination of the Biot-Savart Law dB = Hoi dĩ x ê Ampere's Law 4n r² PB• ds = H, ime > superposition, and symmetry to calculate B at point P as indicated. Note: You must correctly support each step and explain exactly what assumptions you are making. RThe figure on the right shows two parallel loops of wire having a common ât axis. The smaller loop (radius r) is above the larger loop (radius R), by a distance x > R. Assume the magnetic field due to the current i in the larger loop is basically constant over the area of the smaller loop and equal to the value on the axis. 10. Suppose the smaller loop moves away from the larger loop at constant speed: x(t) = xo + Væt, with v, > 0, xo > 0. a) assuming its resistance is 12. Ignore any retardation effect. Find the magnitude and direction of the induced current in the smaller loop b) Is there a time t where the induced current is 0? Explain carefully your answer, using thAux of B.
- X R The figure above shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distance x >> R. Consequently, the magnetic field due to the counterclockwise current i in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at the constant rate dx/dt = V. NOTE: Express your answers to parts (a) and (b) in terms of the given variables. (a) Find an expression for the magnetic flux through the area of the smaller loop as a function of x. ÞB(x) = (b) Determine the magnitude of the induced emf in the smaller loop. E = (c) Determine the direction of the current in the small loop. Choose one ▾a bar magnet is brought closer to a conducting wire loop with 7Ω of resistance. As a result a uniform 3 A current is induced in the wire. What is the rate at which the external magnetic flux is changing indies the wire loop? Explain the reasoning behind your selection in detail. A) 5 T m2/sB) 10.5 T m2/sC) 21 T m2/sD) 42 T m2/sE) 84 T m2/s(Figure 1) shows a circuit with an area of 0.070 m² containing a R = 1.0 N resistor and a C = 230 µF uncharged capacitor. Pointing into the plane of the circuit is a uniform magnetic field of magnitude 0.11 T. In 1.0 × 10-2 s the magnetic field strengthens at a constant rate to become 0.80 T pointing into the plane. Part A What maximum charge (sign and magnitude) accumulates on the upper plate of the capacitor in the diagram? Express your answer to two significant figures and include appropriate units. µA ? Value Units Submit Request Answer Provide Feedback Figure 1 of 1 R
- The magnetic field B at all points within the colored circle of the figure (Figure 1)has an initial magnitude of 0.700 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of 0.0300 T/s. Figure X X X X X B X /b X 1 of 1 10.0 cm Part C What is the current in the ring if its resistance is 4.00 $? ΑΣΦ I = Submit Part D X Incorrect; Try Again; 5 attempts remaining What is the emf between points a and b on the ring? ε = Previous Answers Request Answer Submit Part E ΠΙΑΣΦ Request Answer ? IVE ΑΣΦ ? A If the ring is cut at some point and the ends are separated slightly, what will be the emf between the ends? ? Vb.) Find the net magnetic field at P. 10.) When a magnetic field is first turned on, the magnetic flux through a 10-turn coil varies over time. The equation for the magnetic flux is m = 200.0t2 – 120.0t, where the magnetic flux is measured in webers, and the t is in minutes. The loop is in the plane of the page, with the unit normal pointing out of the page. dºm a.) Calculate an expression for dt b.) Find an equation for the induced emf as a function of time.You would like to store 7.9 J of energy in the magnetic field of a solenoid. The solenoid has 570 circular turns of diameter 7.4 cm distributed uniformly along its 24 cm length. Part A How much current is needed? Express your answer using two significant figures. I= 26.26 VE ΑΣΦ Submit Previous Answers Request Answer Part B X Incorrect; Try Again; 29 attempts remaining B B= 0.0783 What is the magnitude of the magnetic field inside the solenoid? Express your answer using two significant figures. ΑΣΦ Part C Submit Previous Answers Request Answer UB= ? PRZEZ * Incorrect; Try Again; 29 attempts remaining ? A What is the energy density (energy/volume) inside the solenoid? Express your answer using two significant figures. VE ΑΣΦ PRZ ? T kJ/m³