Consider the system pictured in the figure below. A 14.9-cm horizontal wire of m

Question

Consider the system pictured in the figure below. A 14.9-cm horizontal wire of mass 16.4 g is placed between two thin, vertical conductors, and a uniform magnetic field acts perpendicular to the page. The wire is free to move vertically without friction on the two vertical conductors. When a 4.95-A current is directed as shown in the figure, the horizontal wire moves upward at constant velocity in the presence of gravity.

(a) What forces act on the horizontal wire? (Select all that apply.)

electric forcegravitational forcemagnetic force

(b) Under what condition is the wire able to move upward at constant velocity?

(c) Find the magnitude and direction of the minimum magnetic field required to move the wire at constant speed.

(d) What happens if the magnetic field exceeds this minimum value?

magnitude in T direction (Select---out of the screeninto the screen up left right down ) Consider the system pictured in the figure below. A 14.9-cm horizontal wire of mass 16.4 g is placed between two thin, vertical conductors, and a uniform magnetic field acts perpendicular to the page. The wire is free to move vertically without friction on the two vertical conductors. When a 4.95-A current is directed as shown in the figure, the horizontal wire moves upward at constant velocity in the presence of gravity. (a) What forces act on the horizontal wire? (Select all that apply.) (b) Under what condition is the wire able to move upward at constant velocity? (c) Find the magnitude and direction of the minimum magnetic field required to move the wire at constant speed. (d) What happens if the magnetic field exceeds this minimum value?

Explanation / Answer

Part A: forces acting on the horizontal wire include: magnetic and gravitational force.

Part B: When the magnetic force is upward and balances the downward gravitational force, the net force on the wire is zero, and the wire can move upward at constant velocity.

Part C: To find the magnitude and direction of the minimum magnetic field, write out the forces acting along the y-direction:

Forces along y = magnetic force - m*g = 0 (*where m=mass, g=gravity)

magnetic force = I*L*B (*where I=current, L=length, B=magnetic field)

plugging this into the equation we get:

Forces along y = I*L*B - m*g = 0

this can rewritten as :

I*L*B = m*g

Solving for B, we get:

B = (m*g) / I*L
= (16.4*9.8)/(4.95*14.9)
B=2.17 T
Part D: The field exceeds the magnitude above, the upward magnetic force exceeds the downward force of gravity, so the wire accelerates upward.

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