Question

3. A certain horizontal east-west lined wire has a mass of 0.2kg per meter of length and carries a current I. Impressed on the wire is northward-directed horizontal magnetic field strength of 0.4T. Find the current I if the magnetic force is to support the weight of the wire? (use: g = 10m/s?)(3pts)​

Answer 1

i = 4.9 A

Step-by-step explanation:

The expression for the magnetic force in a wire carrying a current is

F = i L x B

bold letters indicate vectors.

The direction of the cable is towards the East, the direction of the magnetic field is towards the North, so the vector product is in the vertical direction (z-axis) upwards and the weight of the cable is vertical downwards. Let's apply the equilibrium condition

F - W = 0

i L B = m g

They indicate the linear density of the cable λ = 0.2 kg / m

λ = m / L

m = λ L

we substitute

i B = λ g

i =
`( \lambda \ g)/(B)`

let's calculate

i = 0.2 9.8 / 0.4

i = 4.9 A