Calculate the magnitude of magnetic field at a distance r from the axis where: . r < a .ab
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- A wire with resistivity ρ (resistance per unit length) is bended in a way to form a shape like bb-8 in the movie Star Wars. (See the figure on the right.) We can approximate it as two circles of radius R and 2R lying in the same plane. Note the wire has an insulating shell, and it crosses over itself at joint of the two circles. The wire is then placed in a magnetic field that is spatially uniform, but increases its magnitude over time with B = bt, where b is a constant of appropriate dimension. (a) What is the total resistance of the wire? Express your answer in terms of ρ and R. (b) What is the emf induced in the upper circle? In which direction? Express your answer in terms of R and b. (c) What is the emf induced in the lower circle? In which direction? Express your answer with R and b. (d) Find the net induced current flowing in the wire. Also specify the direction of the induced current. (It is better to indicate the direction by drawing arrows on the figure…Calculate the magnetic field intensity inside and outside of a very long wire of radius R which is carrying a uniformly distributed total current of / in z-direction.Consider a thin current-carrying wire as shown in the figure on the left. The wire carries a current of 2 mA and consists of a circular part of radius 0.4 cm and a sweeping angle of 45º, and two straight portions extending to infinity in the radial direction of the circular part. (a)Using Biot-Savart law, derive an equation for the magnitude B of the magnetic field at the center of its circular portion (i.e. at point P) in terms of the known quantities of the problem and indicate its direction. (b) Then, use this formula to find a numerical result for B.
- For a cylindrical conductor with a hollow center, let the radius from the axis to the inner circle be a and the radius from the axis to the outer circle be b , as shown below. Note that the region from the axis to a is hollow while the region between a and b is a conductor. We assume that the current I in the cylindrical conductor is uniformly spread into the cross-section between a and b Calculate the magnitude of magnetic field at a distance from the axis where: • r b Plot the magnitude of the magnetic field with respect to the distance r from the axis.A toroid is a solenoid bent into the shape of a doughnut. It looks similar to a toy Slinky® with ends joined to make a circle. Consider a toroid consisting of N turns of a single wire with current I flowing through it. (Figure 1) Consider the toroid to be lying in the re plane of a cylindrical coordinate system, with the z axis along the axis of the toroid (pointing out of the screen). Let represent the angular position around the toroid, and let r be the distance from the axis of the toroid. For now, treat the toroid as ideal; that is, ignore the component of the current in the direction. Figure 00 Ampèrean loop (a) 1 of 1 (b) Correct Notice that the direction is antiparallel to the path shown by the Ampèrean loop in the figure. Also, by definition, ✩ × î = Ô. Part C What is B (r), the magnitude of the magnetic field inside the toroid and at a distance r from the axis of the toroid? Express the magnetic field in terms of I, μo (the permeability of free space), N, and r. ► View…A long, horizontal wire is carrying a current I. A particle of mass m and charge q is fired horizontally at a speed v0. The initial velocity of the particle is parallel to the wire, and its initial position is a distance r directly below the wire, as shown in (Figure 1). What initial speed must the particle have for it to travel in a straight line? Do not ignore gravity. Express your answer in terms of I, m, q, r, µo, and the acceleration of gravity g. Part I Determine at what initial speed vo the particle will travel in a straight horizontal line. Express your answer in terms of some, all, or none of the variables m, q, vo, I, r, and the constants 9, Ho, and T. ► View Available Hint(s) v0 = VE ΑΣΦ Review | Constants ?
- You are facing a loop of wire which carries a clockwise current of 3.0A and which surrounds an area of 600 cm2. Determine the torque (magnitude and direction) if the flux density of 2 T is parallel to the wire directed towards the top of this page.A closed current path is made from two different circular arcs as shown in the figure below. The larger arc has radius 3.0 cm and covers one quarter of the circle, and the smaller arc has radius 1.0 cm and covers the remaining three quarters of the circle. If the current is 1.5 A going counterclockwise, what is the magnitude of the B-field at the center of the circular arcs? Express your answer to the nearest µT.Question A5 Consider an infinitely large sheet lying in the zz-plane at the origin, the extent of the sheet in the x, and z direction is infinite. The sheet carries surface current J = Jok, where Jo is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.
- A rectangular wire loop of height h, width w, and net electrical resistance R lies in the x-y plane. As shown in the figure below, the entire region x < 0 of space is occupied by a constant, uniform magnetic field which points in the –z direction (into the page). In order to determine the magnitude of this field, a student pulls the wire loop out of the magnetic field region at a constant velocity v in the +x-direction, and measures the current I induced in the loop during this process. I = 17 μAR = 35 ohmsh = 3 cm w = 8 cmv = 2 cm/sec a) What is the direction of the current induced in the wire loop? b)What is the magnitude B of the magnetic field?Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.Q1: What current density would produce the vector potential, Ã = k r ê (where k is a constant), in spherical coordinates. Q2: Find the magnetic field at the centre of an Equilateral triangle loop which carries a steady current I. Let R be the distance from centre to side.