Answer:
Explanation:
Given that,
Resistivity p = 1.59 × 10^-8 Ω·m
Length of coil L = 23m
Voltage across solenoid V = 3V
Magnetic field B = 6.69 × 10^-3 T.
Radius of wire r=?
Magnetic field is give as
B = μo•i•n
Where n is number of turns per length, then, n= N/L
N = L/2r
Therefore, n = 1/2r
So, B = μo•i/2r
Then, r = μo•i/2B
From ohms law
V=iR
i= V/R
So, r = μo•V/2R•B
Our resistance is given as
R = pL/A
Then, we have
r = μo•V/2R•B
r = μo•V•A/2•p•L•B
A is the area and it is given as
A = πr²
r = μo•V•πr²/2•p•L•B
Then, making r subject of formula
r = 2•p•L•B / μo•V•π
r = (2×1.59×10^-8×23×6.69×10^-3) / (4π×10^-7 × 3× π)
r = 4.13 × 10^-4m
The radius of the wire is 4.13×10^-4m
Answer: 4.14*10^-4 m
Explanation:
n = N / L, where N = l/2r. So that
n = (l/2r) / L
n = 1/2r
Also, we know that
B = μnI. Substituting for n, we have
B = μI / 2r. If we make r subject of formula
r = μI / 2B
Recall, V = IR, and I = V/R, substituting for I
r = μV / 2BR
Also, ρ = RA/L, and R = ρL / A
substituting R also, we have
r = μVA / 2BρL
A can also be represented as, πr², so that we have
r = μVπr² / 2BρL
1 = μVπr / 2BρL, making r subject of formula again, we have
r = 2BρL / μVπ
r = (2 * 6.69*10^-3 * 1.59*10^-8 * 23) / (4π*10^-7 * 3 * π)
r = 4.89*10^-9 / 1.18*10^-5
r = 4.14*10^-4 m
