A 65-cm segment of conducting wire carries a current of 0.35 A. The wire is placed in a uniform magnetic field that has a magnitude of 1.24 T. What is the angle between the wire segment and the magnetic field if the force on the wire is 0.26 N? a. 37°.
b. 43°.
c. 23°.
d. 53°.
e. 67°.

e) 67°

Explanation:

the force on the wire can be calculated using the expression below

F = BILsinФ

But we are looking for the angle between the wire segment and the magnetic field, then we can make Ф the subject of the formula from the above expresion, then we have,

Ф =sin⁻¹ (F/BIL)

The parameters is defined as

I =current that is been carried by the wire= 0.35 A

Ф = angle between the wire segment and the magnetic field, which is the unknown?

L = length of the wire=65 cm

B = magnetic field = 1.24

F= force on the wire = 0.26 N,

Ф =sin⁻¹ (F/BIL)

Ф =sin⁻¹ X eqn(#)

Where X= (F/BIL)

We can calculate for X= (F/BIL), from eqn(#) by substituting value of Force, Lenght and

magnetic field

X=(F/BIL)= 0.26/(1.24×0.35×0.65)

= 0.26/0.2821

=0.922

Then substitute X into eqn (Ф =sin⁻¹ X)

Then

Ф =sin⁻¹ (0.922)

Ф=66.42°

Ф=67° approximately

Therefore, the angle between the wire segment and the magnetic field is 67°

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