Question

1. a) You have a maximum magnetic field of 1.45 x 10^(-5) Tesla when measured 3.0 cm away from the long section of wire. What is the maximum current that must flow through the wire to create this B-field?

b) You want to make sure you clearly see the time dependence on your phone’s app, decide to design the RC portion of your circuit so that it takes 1.0 seconds for the current to decrease to 10.% of its maximum value. What is the time constant needed?

Answer 1

1.

a.)

Magnetic field due to a current carrying wire at 'd' distance is given by,

B = *I/(2*pi*d)

here, = 4*pi*10^-7

I = current in wire = ??

d = distance from wire = 3.0 cm = 0.03 m

B = magnetic field = 1.45*10^-5 Tesla

then, I = 2*pi*d*B/ = 2*pi*0.03*(1.45*10^-5)/(4*pi*10^-7)

I = 2.175 Amp = minimum current in wire

b.)

Current in discharging RC circuit is given by,

I = I0*e^(-t/)

here, I0 = maximum current in circuit

t = time 1.0 seconds

I = current in circuit = 10% of maximum current = 0.10*I0

= time constant = ??

then, 0.10*I0 = I0*e^(-t/)

e^(-t/) = 0.10

-t/ = ln(0.10)

= -t/ln(0.10) = -1.0/ln(0.10)

= 0.434 sec.