Question

A wire having a mass per unit length of 0.600 g/cm carries a 1.90 A current horizontally to the south.

(a) What is the direction of the minimum magnetic field needed to lift this wire vertically upward?

(b) What is the magnitude of the minimum magnetic field needed to lift this wire vertically upward?

Answer 1

(a) The direction of magnetic field will be east.

(b) The minimum magnetic field needed is 0.309 Tesla.

Step-by-step explanation:

Given the mass per unit length of the wire is 0.600 g/cm.

And it carries 1.90 A current horizontally to the south.

The formula of magnetic force per unit length on current carrying conductor is

`(F_m)/(L) =BIsin(\theta )` Equation(1)

Where,

`F_m` is the magnitude of magnetic force.

`B` is the magnetic field.

`I` is the current on wire, given as 1.90 A

`L` is the length of the wire.

`\theta` is the angle between current and the magnetic field. For our problem
`\theta` will be 90°.

Also, the gravitational force per unit length is

`(F_g)/(L)=((m)/(L) )g` Equation(2)

Where,

`m` is the mass of the wire.

`g` is the acceleration due to gravity.

Part(a)

Using the right hand rule we can determine the force on a current-carrying wire.

Given the current is flowing horizontally to the south. Pointing our thumb to the south direction, we can see our finger that represents the direction of magnetic field is going in the east direction.

So, the direction of magnetic field will be east.

Part (b)

To lift the conductor vertically Equation(1) and Equation(2) should be equal and in opposite direction.

Hence,

`((m)/(L))g=BIsin(\theta)\\\\B=((m)/(L)) (g)/(Isin(\theta))`

According to the question the mass per unit length of the wire is 0.600 g/cm. We need to convert it in standard unit.

So, 0.600 g/cm will be equal to
`0.600(100)/(1000)\ kg/m=0.06\ kg/m`

Now,
`(m)/(L)=0.06`

`B=0.06* (9.81)/(1.90* sin(90))\\ \\B=0.309\ T`

So, minimum magnetic field needed is 0.309 Tesla.

Answer 2

a) the direction of the magnetic field is east.

b) The magnitude = 0.310 T

Step-by-step explanation:

Step 1: Data given

Mass per unit length = 0.600 g/cm

current = 1.90 horizontally to the south

Step 2:

The force of gravity = magnetic force

m*g = i*L*B

m/L * g = i*B

B = ((m/L)*g) /i

⇒ with m/L = the mass per length unit = 0.600 g/cm = 0.0600 kg /m

⇒ g = 9.81 m/s²

⇒ i = the current = 1.90 A

B = (0.0600 * 9.81) / 1.90

B = 0.310 T

According to the right hand rule, the direction of the magnetic field is east.