Question

When a wire 1.5 m long carries a 24-A current in the +x direction in a uniform external magnetic field, the magnetic force exerted by the field on the wire is given by FBx = 0, FBy = 3.0 N, FBz = 2.0 N. When the wire is rotated until the charge carriers travel in the +y direction, the magnetic force exerted by the field on the wire is given by FBx = -3.0 N, FBy = 0, FBz = -2.0 N. Part A: Determine the components of the magnetic field.Part B: Determine the magnitude of the magnetic field.

Answer 1

The magnetic field components can be determined by dividing the magnetic force components by the length of the wire. The magnitude of the magnetic field can be calculated using the Pythagorean theorem.

Step-by-step explanation:

The magnetic field can be determined by using the formula F = I x B, where F is the magnetic force, I is the current, and B is the magnetic field. Let's consider the first scenario where the charge carriers travel in the +x direction. The magnetic force components in this case are FBx = 0, FBy = 3.0 N, FBz = 2.0 N. Since the wire is 1.5 m long, we can calculate the magnetic field components by dividing the force components by the length of the wire.

Part A:

The components of the magnetic field are: Bx = FBx / length of the wire = 0 / 1.5 = 0 T, By = FBy / length of the wire = 3.0 / 1.5 = 2.0 T, Bz = FBz / length of the wire = 2.0 / 1.5 = 1.33 T.

Part B:

The magnitude of the magnetic field can be calculated using the formula B = sqrt(Bx^2 + By^2 + Bz^2) = sqrt(0^2 + 2.0^2 + 1.33^2) = 2.40 T

Answer 2

Step-by-step explanation:

Let the magnetic field be

B =
`B_xi +B_yj +B_z k`

For magnetic force , the expression is

F = L ( I x B )

= 1.5 ( 24i x
`B_xi +B_yj +B_z k` )

F = 36 B_y k - 36 B_z j

Given

F = 3 j + 2 k

Equating equal terms

we have

B_y = 2 / 36 , B_z = - 3 / 36

Now the direction of current is changed to y direction

so F =
`1.5[ 24j * ( B_xi +B_yj +B_z k )]`

Given

F = - 3 i - 2 k

Equating equal terms

we have

B_x = 2 / 36 , B_z = - 3 / 36

So B = 2/36 i + 2/36 j - 3/ 36 k

Magnitude of B

= 4.1 / 36 T