Discussion problems

Prof. Hanany groups

1- Hall Effect. A non-magnetic metallic object of width w carrying current I is located in a magnetic

field of strength (fig1). Consider the forces on an individual charge. Given that the

charge is moving at velocity v through the material, find the voltage VH which is required for the

forces to be in equilibrium.

fig1. Hall Effect picture from Wikipedia.

2- Solenoid. A solenoid is an apparatus used to produce magnetic field (fig2). A solenoid of length L

and radius R carries current I. Calculate magnetic field all along the axis of the solenoid starting

from Biot-Savart law.

(a) Given that the axis of the solenoid is along the z-axis, consider a small ring of the solenoid of

width dz’. If there are n turns per unit length, write an expression for the current di of the

segment dz’.

(b) Knowing the following formula for the magnetic field along the axis of a single ring of

current I:

find an expression for the field at a point along the z-axis from the current di of part (a).

Put your answer in terms of dz’.

(c) Integrate your expression from part (b) over the length of the solenoid to find a formula for

the magnetic field . Also, show that in the limit that L>>R and L>>z, your expression

reduces to the formula for the field of a “long” solenoid:

fig2. Solenoid picture from Wikipedia.

3- A piece of wire is shaped into two connected concentric arcs with central angle of 120 degrees.

The inner and outer radii of the arcs are a and b, respectively. Calculate the magnetic field at

point P if the shaped wire is carrying current I.

4- An infinitely long, straight wire is bent, as shown in fig3. The circular portion has a radius of 10

cm and its center is a distance r from the straight part. Find the value of r such that the magnetic

field at the center of the circular portion is zero.

fig3. Picture from Tipler-Mosca.

b

a