Question

Can you please help with parts a - d

(10%) Problem 6: Two power lines, line 1 and line 2, both of length LL-58 m, are strung east-west between two towers. line l is r12 2.5 m directly above line 2. The current in both power lines is IL 81 A to the west. Assume the power lines are straight and you can use the approximation r12 < 쇼 25% Part (a) Find the magnitude of the magnetic field B21, in teslas, produced by line l at line 2 Grade Summary Deductions Potential 21 0% 100% Submissions Attempts remaining:6 (0% per attempt) detailed view sin cos tan0 cotan0 asinO acosO atan)a acotan sinh0 coshO tanh0 cotanhO Degrees Radians 0 END ВАС CLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: i Feedback: 1% deduction per feedback 25% Part (b) what is the direction of the magnetic field produced by line 1 at line 2? South. Correct 25% Part (c) Calculate the magnitude of the magnetic force F21-in newtons, that the current in line l exerts on line 2 25% Part (d) Assume a typical power line has a mass of 890 kg per 1000 m. How many times larger would the current in both lines have to be for the magnetic force on the line to balance the force of gravity?

Answer 1

Part A.

B21 = Magnetic field produced by line 1 at line 2

SInce given that r12 <<< L_L, So We can treat wires as infinite length wire

Now Magnetic field due to infinite length wire at a distance r12 from wire is given by:

B21 = u0*i1/(2*pi*12)

i1 = 81 A towards west

r12 = 2.5 m

So,

B21 = 4*pi*10^-7*81/(2*pi*2.5)

B21 = 6.48*10^-6 T

Part B.

From Right hand Rule, direction is towards south

Part C.

Now Magnetic force between two current carrying wires is given by:

F21 = i2*L*B21

i2 = 81 A

L = 58 m

B21 = 6.48*10^-6

So,

F21 = 81*58*6.48*10^-6

F21 = 0.03044 N = 30.44*10^-3 N

Part D.

Now We need current in both lines when magnetic force is balanced by force of gravity

Fm = Fg

i*L*B21 = m*g

B21 = u0*i/(2*pi*r12)

M = mass of wire = 890 kg/1000 m = 0.890 kg/m

mass of 58 m wire will be = M*L = (0.890 kg/m)*58 m = 51.62 kg

g = 9.81 m/s^2

So,

i*L*u0*i/(2*pi*r12) = m*g

i^2 = 2*pi*r12*m*g/(u0*L)

Using known values:

i = sqrt (2*pi*2.5*51.62*9.81/(4*pi*10^-7*58))

i = 10446.83 Amp

Since we need how many times larger than initial given current, So

i/i_L = 10446.83/81

i/i_L = 128.97 Amp = 129 times larger

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