A long straight wire has a current flowing through it. A measurement 1.90 cm fro
ID: 1310334 • Letter: A
Question
A long straight wire has a current flowing through it. A measurement 1.90 cm from the center of the wire shows that the magnetic field at that location is 7.5 microT. Answer the following questions without finding the current: (a) at a distance of 4.0 cm from the center of the wire what will be the magnetic field strength? (b) At what distance from the center of the wire will the magnetic field strength be 1.2 microT? (c) If the current triples, what will be the magnetic field strength at a distance of 2.80 cm from the center of the wire?
Explanation / Answer
As B is inversely proportional to r, we can have the relation B2/B1 = r1/r2
a) B2 = B1r1/r2 = 7.5 x 1.9/4 = 3.5625 mT
b) Let it be r2 and r2 = B1r1 / B2 = 7.5 x 1.9 /1.2 =11.875 cm.
c) B is directly proportional to the current I, So if I is tripled then the field B must also be tripled.
So the value of B at 1.9 cm will be 7.5 x 3 = 22.5 mT
Using the relation in (a) B2 = B1r1/r2 = 22.5 x 1.9 /2.8 = 15.267 mT .