You have a 12-V battery, a set of 10 50- resistors, and a long (2-m) connecting

Question

You have a 12-V battery, a set of 10 50-  resistors, and a long (2-m) connecting wire. Take the thickness of the wire to be 0.6 mmand the radius of solenoid to be 1 cm.

Part A

Estimate the maximum magnitude of the B field that you can produce with this equipment. You can determine the maximum length of the solenoid (L) by calculating the number of turns (N) the wire will permit and multiplying that by the thickness of the wire (assume no space between turns).   

Express your answer to one significant figure and include the appropriate units.

You have a 12-V battery, a set of 10 50-  resistors, and a long (2-m) connecting wire. Take the thickness of the wire to be 0.6 mmand the radius of solenoid to be 1 cm.

Part A

Estimate the maximum magnitude of the B field that you can produce with this equipment. You can determine the maximum length of the solenoid (L) by calculating the number of turns (N) the wire will permit and multiplying that by the thickness of the wire (assume no space between turns).   

Express your answer to one significant figure and include the appropriate units.

Explanation / Answer

B = mu*n*I

mu = 4pi x 10^- 7

n = number of turns / length

I = current = V/R

we have 10 50 ohm resistor , for maximum magnitude of B value of current should be maximum it means equivalent resistance of circuit should be miminum

then all resistor should be in parallel combination

1/Req = 1/R1 + 1/R2 + ......+ 1/R10

1/Req = 1/50 + 1/50 + ...... + 1/50

1/Req = 10/50

Req = 50/10 = 5 ohm

I = V/Req = 12/5

The total number of turns on the solenoid is given by:

N = L / (2pi*r)

L = length of wire

N= L/2pi*r

r = 1 x 10^-2 m

N = 31,847 = 32 turns

n = N/L = 32 /2 = 16 turns/length

B = mu*n*I

B = 4*pi x 10^-7 x 16 x 12/5

B = 4.83 x 10^-5 T

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