The figure below shows two closed paths wrapped around two conducting loops carrying currents in and i2. What is the value of the integral of B for (a) path 1 and (b) path 2?
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- The following picture shows a LONG conductor carrying current I. Nearby there is a conducting rectangular loop with sides a = 8 cm and b = 4 cm. The loop also carries a resistance R = 10 ohms. The current is constant and has a value of I = 6.0 Amperes. The loop is moving away to the right with a constant velocity, V = 2 m/s. Answer the following questions at the instant of time t when the left edge of the loop is at position "x" as shown below Use the coordinate system , x to the right, y into the board, z upward a) Write an expression for the magnetic field the distance "x" (from the LONG conductor to the loop. ) USE “+" for CCW circulation and "-" for CW circulation. a function of b) Write the magnetic field in "i-j-k" format at point "x" to the right of the current carrying wire in the "i-z" plane R. a c) Write the infinitesimal area vector for the loop in "i-j-k" format d) Write the explicit integral for the magnetic flux through the area of the loop using the answer for B and dA…A short rod of length a moves with its velocity v → parallel to an infinite wire carrying a current I (see below). If the end of the rod nearer the wire is a distance b from the wire, what is the emf induced in the rod?Cross-sectional views of three long conductors carrying currents I = 2.6 A, I2 = 2.2 A, and 13 = 5.6 A are shown in the figure below. Determine the closed line integrals O B• de around the five Ampèrian loops a through e as shown in the figure. (Assume positive current is into the page.) de b d de de de loop a T. m loop b T. m loop c T.m loop d T. m loop e T.m
- A rectangular conducting loop of width L, resistance R, and mass m is in a magnetic field B, as indicated in the diagram below. The magnetic field is constant throughout the shaded region (and zero outside the shaded region) and is horizontally oriented into the page. If the loop is dropped, as it crosses the threshold of the magnetic field, it will reach a terminal speed vt. Find an expression for vt (ignoring air drag).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°.Derive an expression for the current in a system like shown, under the following conditions. The resistance between the rails is R , the rails and the moving rod are identical in cross section A and have the same resistivity ρ .The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B . At time zero, the moving rod is next to the resistance R .
- Awire with current i= 3.06 A is shown in the figure. wo semi-infinite straight seCions, both tangent to the same circlewith radius 3.52 cm, are connected by a dircular arc that has acentral angle andruns along the circumference of the circle. The connecting arc and the two straight sections aWlie in the same plane. f B= 0 at thye center of the CArcle whatsR Number units degreesQuestion 1: A) Dinesh studying rail guns has been suggested for launching projectiles into space without chemical rockets. A tabletop model rail gun (Figure 1.) consists of two long, parallel, horizontal rails, l= 6.80 cm apart, bridged by a bar of mass m= 8.00 g that is free to slide without friction. The rails and bar have low electric resistance, and the current is limited to a constant I = 42.0 A by a power supply that is far to the left of the figure, so it has no magnetic effect on the bar. Figure 1 shows the bar at rest at the midpoint of the rails at the moment the current is established. He wishes to find the speed with which the bar leaves the rails after being released from the midpoint of the rails (Hint: you need to draw the figure). (Mo = 4π × 10-¹T.) Jg x V₁ = = 0 m d Figure 1. (i) Find the magnitude of the magnetic field at a distance of 1.85 cm from a single long wire carrying a current of 2.40 A. (ii) For purposes of evaluating the magnetic field, model the rails as…Prove that the relation t = NiAB sin u holds not only for the rectangular loop but also for a closed loop of any shape. (Hint: Replace the loop of arbitrary shape with an assembly of adjacent long, thin, approximately rectangular loops that are nearly equivalent to the loop of arbitrary shape as far as the distribution of current is concerned.)
- A cylindrical magnetic core of radius b, height h conductivity o and permeability u is carrying a magnetic flux density field B = B, sin (@t) as shown in figure. Find the eddy current losses in the cylindrical core B(1)In the figure below, a current i = 28 A is set up in a long hairpin conductor formed by bending a wire into a semicircle of radius R = 9.0 mm. Point b is midway between the straight sections and so distant from the semicircle that each straight section can be approximated as being an infinite wire. (a) What is the magnitude of B (vector) at a? ___________T(b) What is the direction of B (vector) at a? 1) into the page 2) out of the page (c) What is the magnitude of B (vector) at b? ____________T(d) What is the direction of B (vector) at b? 1) into the page 2) out of the page (please show units. It really helps me out)Design a current loop that, when rotated in a uniform magnetic field of strength 0.67 T, will produce an emf E = E, sin(wt), where E, = 110 V and w = 120n rad/s. First, choose the number of turns the loop should have. (Enter a positive integer less than 100.) turns Then calculate the needed area of the loop (in m2). (Use the number of turns you entered above.) m2