Question

The force on a wire is a maximum of 4.30 N when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. he wire is observed to "jump" toward the observer when the current is turned on. If the pole faces have a diameter of 10.2 cm, estimate the current in the if the field .188 T 24×10^2 the wire is tipped so that it now makes an angle of 13.5∘ with the horizontal, what force will it now feel? Two variables changed due to the tipping. 1. The angle between the current and the magnetic is no longer 90 deg. (Note: It is not 13.5 deg.) 2 . The length of the wire in the nagnetic field also changed. Use trigonometry to find the length of the wire in the magnetic field. Tries 9/30 Previous Tries

Answer 1

To estimate the current in the wire when it is tipped, trigonometry must be used to determine the new effective length of the wire in the magnetic field and the new angle of interaction. The cosine of the tipping angle gives the effective length, and the angle between the current and the field is adjusted accordingly to recalculate the force.

Step-by-step explanation:

The student's question involves calculating the force experienced by a wire with an electric current, placed in a magnetic field. Initially, the wire is horizontal and experiences maximum force at a 90-degree angle to the magnetic field. When the wire is tipped by 13.5 degrees, both the angle of interaction and the length of the wire within the magnetic field are altered. To find the new force, one must use trigonometry to calculate the effective length of the wire within the magnetic field's influence and account for the change in the angle between the current and the field.

With the initial setup, the force on the wire is given by the formula F = I * L * B * sin(θ), where F is the force in newtons (N), I is the current in amperes (A), L is the length of the wire in the field in meters (m), B is the magnetic field strength in teslas (T), and θ is the angle between the current and magnetic field.

When tipped at an angle, the effective length of the wire that is within the field can be found using the cosine of the tipping angle. If we assume the full diameter is within the field, then L_eff = diameter * cos(13.5). The angle θ also changes to 90 degrees minus the tipping angle; hence θ_eff = 90 - 13.5. One can then recalculate the force as F_new = I * L_eff * B * sin(θ_eff).

Answer 2

The force experienced by a current-carrying wire in a magnetic field depends on the current, the length of the wire within the field, the strength of the magnetic field, and the angle between the wire and the field. The force can be calculated using the equation F = I * L * B * sin(θ) and adjusting for changes in the wire's position using trigonometry.

Step-by-step explanation:

The force experienced by a wire carrying current in a magnetic field is given by the equation F = I * L * B * sin(θ), where F is the force, I is the current in the wire, L is the length of the wire within the magnetic field, B is the magnetic field strength, and θ is the angle between the current direction and the magnetic field.

When the wire is tipped and makes an angle of 13.5° with the horizontal, the magnetic field is still perpendicular, therefore θ = 90° - 13.5° = 76.5°. To find the length of the wire within the field after tilting, we can use trigonometry. Assuming the diameter of the pole faces is the relevant length, we have:

L' = L * cos(13.5°)

To find the new force:

F' = I * L' * B * sin(76.5°)

As we don't have the current value, we can express it in terms of maximum force. When the wire was horizontal and θ was 90°:

F(max) = I * L * B

Thus, the current is:

I = F(max) / (L * B)

Substituting I in the equation for F' gives:

F' = (F(max) / (L * B)) * L' * B * sin(76.5°)