(a) Find the magnetic field at the center of a square loop, which carries a steady current I. Let R be the distance from center to side. (b) Find the magnetic field at point P for the steady current configurations shown in the Figure below. R

A wire ismade into a circular shape of radius R and pivoted along a central support.The two ends of the sire are touching a banish that is connected to a &power source. The stricture is between the poles of a magnet such that we can assume there is a uniform magnetic field on the wire. In terms of a coordinate system with origin at the center ofthe ring, magneticfieldisBx=B0,By=Bz= 0. and the ring rotates about the z-axis. Find the torque on the ring siren it is not in the xz-plane.

What is the magnetic field at P due to the current I in the wire shown?

Consider the axial magnetic field Bv=0IR2/2(y2+R2)3/2 of the circular current loop shown below. (a) Evaluate aaBydy Also show that limaaaBydy=0I (b) Can you deduce this limit without evaluating the integral? (Hint: See the accompanying figure.)

A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be 1.5103V/m (a) What is the drift speed of the conduction electrons? (b) Assuming that n =8.01028 elections per cubic meter and that the cross-sectional area of the strip is 5.0106m2 , calculate the current in the ship, (c) What is the Hall coefficient 1/nq?

A rectangular copper ring, of mass 100 g and resistance 0.2 1, is in a region of uniform magnetic field that is perpendicular to the area enclosed by the ring and horizontal to Earth’s surface. The ring is let go from rest when it is at the edge of the nonzero magnetic field region (see below). (a) Find its speed when the ring just exits the region of uniform magnetic field. (b) If it was let go at t = 0, what is the time when it exits the region of magnetic field for the following values: a=25cm,b=50cmB=3T , and g=9.8m/s2 ? Assume the magnetic field of the induced current is negligible compared to 3T.

The current density in the long, cylindrical wire shown in the accompanying figure varies with distance r from the center of the wire according to J = cr. where c is a constant (a) What is the current through the wire? (b) What is the magnetic field produced by this current for r < R? For rR ?

The square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. (a) Wliat is the frequency' of the output voltage? (b) What is the strength of the magnetic field in which the coil is turning?

Unreasonable results Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (C) Which premise is responsible?

A 500-turn coil with a 0.250m2 area is spun in Earth’s 5.00105T magnetic field, producing a 12.0-kV maximum emf. (a) As what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?