AP Physics C Chapter 28 & 29 Take Home4/11/2012

1.The figure (not drawn to scale) shows a square loop, 20 cm on a side, in the xy plane with its center at the origin. The loop carries a current of 5 A. l Above it at y = 0, z = 10 cm is an infinitely long wire parallel to the x axis carrying a current of 10 A.

a)Find the torque on the loop. Draw an axis for the torque and indicate the direction for the torque about the axis.

b)Find the net force on the loop and indicate its direction on the figure.

2.An infinitely long, straight wire is bent as shown in the figure. The circular portion has a radius of 10 cm with its center a distance r from the straight part. Find r such that the magnetic field at the center of the circular portion is zero.

3.1990E2. In the mass spectrometer shown above, particles having a net charge +Q are accelerated from rest through a potential difference in Region I. They then move in a straight line through Region II, which contains a magnetic field B and an electric field E. Finally, the particles enter Region III, which contains only a magnetic field B, and move in a semicircular path of radius R before striking the detector. The magnetic fields in Regions II and III are uniform, have the same magnitude B, and are directed out of the page as shown.

a.Indicate the direction of the electric field necessary for the particles to move in a straight line through Region II.

b.In terms of any or all of the quantities Q, B, E, and R, determine an expression for the speed v of the charged particles as they enter the Region III.

c.In terms of any or all of the quantities Q, B, E, and R, determine an expression for the mass of the charged particles.

d.In terms of any or all of the quantities Q, B, E, and R, determine an expression for the accelerating potential V in Region I.

e.In terms of any or all of the quantities Q, B, E, and R, determine an expression for acceleration of the particles in Region III.

f.In terms of any or all of the quantities Q, B, E, and R, determine an expression for the time required for the particles to move along the semicircular path in Region III.

4.A coaxial cable consists of a solid inner conductor of radius R1, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3. The conductors carry equal and opposite currents Io distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for

a) rR1

b)R1 < r < R2

c)R2 < r < R3

d)r > R3

e)Draw a sketch for B vs r for 0<r<∞.

5.The figure shows an arrangement knows as a Helmholtz coil. It consists of two circular coils, each of 200 turns and radius R=25.0 cm, separated by a distance s = R. The two coils carry equal currents I = 12.2 mA in the same direction. Find the magnitude of the net magnetic field at P, mid-way between the coils.

6.Three wires are aligned perpendicular to the page, separated from each other by a distance s. The outer wires each carry a current I into the page, and the central wire carries a current 2I out of the page. Find the force per unit length on each wire in terms of s, I and the magnetic constant, and indicate the direction of each force on the appropriate wire in the diagram (that is, up, down, to the left or to the right).

7. Consider Helmholz coils as in the previous problem, where each coil now consists of N turns and radius R, separated by a distance s (s and R are not necessarily equal, whereas they were in the previous problem). The two coils carry equal currents I in the same direction.

a)Show that the first derivative of the magnitude of the net magnetic field of the coils (dB/dx) vanishes at the midpoint P regardless of the value of s.

b)Show that the second derivative (d2B/dx2) also vanishes at P, provided s=R. This accounts for the uniformity of B near P for this particular coil separation.

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