Review. (a) Show that a magnetic dipole in a uniform magnetic field, displaced from its equilibrium orientation and released, can oscillate as a torsional pendulum (Section 15.5) in
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Physics for Scientists and Engineers
- A metal rod of mass m slides without friction along two parallel horizontal rails, separated by a distance l and connected by a resistor R, as shown in Figure P23.15. A uniform vertical magnetic field of magnitude B is applied perpendicular to the plane of the paper. The applied force shown in the figure acts only for a moment, to give die rod a speed v. In terms of m, l, R, B, and v, find the distance the rod will then slide as it coasts to a stop.arrow_forwardWithin the green dashed circle show in Figure P30.21, the magnetic field changes with time according to the expression B = 2.00t3 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P, which is at a distance r = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero? Figure P30.21arrow_forwardThe homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P23.21. A uniform magnetic field is applied perpendicular to the plane of the disk. Assume the field is 0.900 T, the angular speed is 3.20 103 rev/min, and the radius of the disk is 0.400 m. Find the emf generated between the brushes. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion.arrow_forward
- A 2.40 mH toroidal solenoid has an average radius of 6.80 cm and a cross-sectional area of 2.80 cm2. How many coils does it have? In calculating the flux, assume that B is uniform across a cross section, neglect the variation of B with distance from the toroidal axis.arrow_forwardYou are given a straight piece of conductor that is 5.0 cm long and moves in a region of uniform magnetic field of 1.6 T along the z-direction. If the conductor is oriented along the x-axis and moves in the y-direction with a velocity of 5.0 m/s, find the magnitude of induced voltage that will be produced between the ends of this moving conductor.arrow_forwardMagnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?arrow_forward
- A magnetic compass has its needle, of mass 0.050 kg and length 4.0 cm, aligned with the horizontal component of Earth’s magnetic field at a place where that component has the value Bh = 16 mT. After the compass is given a momentary gentle shake, the needle oscillates with angular frequency v = 45 rad/s. Assuming that the needle is a uniform thin rod mounted at its center, find the magnitude of its magnetic dipole moment.arrow_forwardA conducting rod spans a gap of length L = 0.234 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.35 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At2, where A = 2.5 m/s4. The resistance in the wire is R = 25 Ω. Express the derivative of the magnetic flux, dΦ/dt, in terms of B, A, L and t.arrow_forward)A flat circular loop of radius 1.49 m is rotating in a uniform magnetic field of 1.46 T. Find the magnetic flux, in T m2, through the loop when the plane of the loop and the magnetic field vector are perpendicular.arrow_forward
- A conducting rod spans a gap of length L = 0.065 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field with magnitude B = 0.75 T pointing into the paper is in the region. The rod is pulled to the right by an external force, and moves with constant speed v = 0.015 m/s. The resistance in the wire is R = 180Ω. Part (a) Express the magnitude of the magnetic flux going through the loop, Φ, in terms of B, a and L. Part (b) Express the change in the magnetic flux, ΔΦ, in terms of B, L, v and Δt. Part (c) Express the magnitude of the average emf induced in the loop, ε, in terms of B, L, v. Part (d) Calculate the emf, in volts. Part (e) Express the current induced in the loop, I, in terms of ε and R.arrow_forwardWhat current is required in the windings of a solenoid that has 900 turns evenly distributed over a length of 0.5 m, to produce in the center of the solenoid a magnetic field of magnitude 7X10-3 T?arrow_forwardA ring of mass m = 2 g rolls without slipping on a non-conducting horizontal surface with constant speed, which has a uniform distribution of charges. After connecting a uniform horizontal magnetic field B = 0.2 T perpendicular to the plane of the ring, the pressure force of the ring on the surface decreases by half. Determine the speed with which the ring rolls if its total charge is q = 2 μ c (2 x 10-6 c )arrow_forward
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