# PHYS 222 Worksheet 15 Magnetic Field Applications ANSWERS

```PHYS 222
Worksheet 15 – Magnetic Field
Applications
Supplemental Instruction
Iowa State University
Course: PHYS 222
Instructor: Dr. Paula Herrera-Sikl&oacute;dy
Date: 2/23/12
Useful Equations
d F  Idl  B
F  I L B
Magnetic force on an infinitesimal wire section
Magnetic force on a straight wire segment
Related Problems
1) A long wire carrying 4.50 A of current makes two 90 bends, as shown in the figure . The
bent part of the wire passes through a uniform 0.242 T magnetic field directed as shown in
the figure and confined to a limited region of space. Find the magnitude and direction of the
magnetic force on the wire. (Book 27.35)
F  I L B
0.6   0  Fx  0.0726
F  4.50  0.3   0   Fy  0.1452  F  0.07262  0.14522  0.7305 N
0.0  0.242 Fz 
0
 0.1452 
  tan 1 
  63.43 
 0.0726 
2) A thin, 51.0 cm long metal bar with mass 760 g rests on, but is not attached to, two
metallic supports in a uniform magnetic field with a magnitude of 0.460 T, as shown in the
figure . A battery and a resistor of resistance 26.0 Ω are connected in series to the
supports. (Book 27.39)
(a) Determine the largest voltage the battery can have without breaking the circuit at the
supports?
F  I L B
V
I
R
V
 F  LB
R
F  ma  ma 
V
LB
R
maR
, a  9.81 m / s 2
LB
V  825 V
V 
(b) The battery voltage has the maximum value calculated in part (a). If the resistor
suddenly gets partially short-circuited, decreasing its resistance to 2.60 Ω, find the initial
acceleration of the bar.
V 825
I

 317.308 A
R2 2.6
F  ILB  74.44 N
ma  F  Fg  a 
 F  F   88.2 m / s
g
2
m
3) What is the magnitude and direction of the magnetic
force on this segment of wire in a magnetic field of B?
dF  Idl  B
dl  B  2  Rd B cos  
dF  2 IRB cos  d
 /2
 Fy  4 IRB  cos  d  4 IRB
0
```