please answer and put unit of measurement.
Homework 2 4) In the figure, two circular arcs have radii a = 15.0 cm and b = 11.1 cm, subtend angle θ = 79.0°, carry current i = 0.303 A, and share the same center of curvature P. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at P? A) Number Units B) 5) Figure (a) shows two wires, each carrying a current. Wire 1 consists of a circular arc of radius R = 0.018 m and two radial lengths; it carries current i1 = 2.3 A in the direction indicated. Wire 2 is long and straight; it carries a current i2 that can be varied; and it is at distance R/2 from the center of the arc. The net magnetic field B→ due to the two currents is measured at the center of curvature of the arc. Figure (b) is a plot of the component of B→ in the direction perpendicular to the figure as a function of current i2. The horizontal scale is set by i2s = 2.0 A. What is the angle subtended by the arc? Number Units 6) In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 16 cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3, and each wire carries 17 A. What is the magnitude of the net magnetic field at the square's center? Number Units 7) In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a = 10.5 cm. Each wire carries 8.50 A, and the currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3. In unit-vector notation, what is the net magnetic force per meter of wire length on wire 4? Number Units 8) In the figure, a long straight wire carries a current i1 = 37.2 A and a rectangular loop carries current i2 = 20.9 A. Take a = 0.779 cm, b = 8.38 cm, and L = 40.9 cm. What is the magnitude of the net force on the loop due to i1? Number Units 9) The figure shows a cross section across a long cylindrical conductor of radius a = 2.09 cm carrying uniform current 54.6 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 1.22 cm, (c) 2.09 cm (wire's surface), (d) 3.56 cm? A) Number Units b) Number Units c) Number Units d) Number Units 10) The figure shows two closed paths wrapped around two conducting loops carrying currents i1 = 6.8 A and i2 = 3.3 A. What is the value of the integral for (a) path 1 and (b) path 2? A) Number Units b) Number Units 11) A solenoid that is 118 cm long has a radius of 1.86 cm and a winding of 1400 turns; it carries a current of 4.76 A. Calculate the magnitude of the magnetic field inside the solenoid. A) Number Units 12) A student makes a short electromagnet by winding 510 turns of wire around a wooden cylinder of diameter d = 4.2 cm. The coil is connected to a battery producing a current of 4.5 A in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance z >> d will the magnetic field have the magnitude 3.8 µT (approximately one-tenth that of Earth's magnetic field)? A) Number Units b) Number Units 2) A wire loop of radius 12 cm and resistance 7.5 Ω is located in a uniform magnetic field that changes in magnitude as given in the figure. The loop's plane is perpendicular to the magnetic field. What is the magnitude of the emf in volts induced in the loop during the time intervals (a) t = 0 to 2.0 s; (b) 2.0 s to 4.0 s; and (c) 4.0 s to t = 6.0 s? A) Number Units b) Number Units c) Number Units 3) A square wire loop with 2.1 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in the figure. The loop contains an ideal battery with emf = 22 V. If the magnitude of the field varies with time according to B = 0.035 - 0.88 t, with B in teslas and t in seconds, what are (a) the net emf in the circuit and (b) the direction of the (net) current around the loop? A) Number Units b) clockwise or counter clockwise? 4) In the figure, a metal rod is forced to move with constant velocity along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude B = 0.478 T points out of the page. (a) If the rails are separated by 20.1 cm and the speed of the rod is 68.9 cm/s, what is the magnitude of the emf generated in volts? (b) If the rod has a resistance of 22.5 Ω and the rails and connector have negligible resistance, what is the current in amperes in the rod? (c) At what rate is energy being transferred to thermal energy? A) Number Units b) Number Units c) Number Units 5) The figure below shows two circular regions R1 and R2 with radii r1 = 20.6 cm and r2 = 33.3 cm. In R1 there is a uniform magnetic field of magnitude B1 = 50.8 mT directed into the page, and in R2 there is a uniform magnetic field of magnitude B2 = 78.4 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 10.5 mT/s. Calculate ∮E→⋅ds→ for (a) path 1, (b) path 2, and (c) path 3. A) Number Units b) Number Units c) Number Units 6) A circular coil has a 14.2 cm radius and consists of 40.0 closely wound turns of wire. An externally produced magnetic field of magnitude 3.82 mT is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns? (b) When the current in the coil is 4.75 A in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil? A) Number Units b) Number Units 7) The current i through a 4.7 H inductor varies with time t as shown by the graph of the figure. The inductor has a resistance of 16 Ω. Find the magnitude of the induced emf ε during the time intervals (a) t = 0 to 2 ms; (b) 2 ms to 5 ms, and (c) 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.) A) Number Units b) Number Units c) Number Units 8) The current in an RL circuit builds up to one-third of its steady-state value in 4.18 s. Find the inductive time constant. A) Number Units 9) In the figure, ε = 106 V, R1 = 12.6 Ω, R2 = 25.3 Ω, R3 = 27.4 Ω, and L = 2.73 H. Immediately after switch S is closed, what are (a) i1 and (b) i2? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative values.) A long time later, what are (c) i1 and (d) i2? The switch is then reopened. Just then, what are (e) i1 and (f) i2? A long time later, what are (g) i1 and (h) i2? A) Number Units b) Number Units c) Number