How Fast Can an MRI's Magnetic Field Safely Shut Off to Prevent Harm?

[rcmango]

Homework Statement

Magnetic resonance imaging (MRI) is a medical technique for producing "pictures" of the interior of the body. The patient is placed within a strong magnetic field. One safety concern is what would happen to the positively and negatively charged particles in the body fluids if an equipment failure caused the magnetic field to be shut off suddenly. An induced emf could cause these particles to flow, producing an electric current within the body. Suppose the largest surface of the body through which flux passes has an area of 0.028 m2 and a normal that is parallel to a magnetic field of 2.0 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V.
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Homework Equations

The Attempt at a Solution

not sure what I'm doing wrong, but i can't find an answer for this.

I have these formulas: E = -N * chng in flux/chang in time
also, flux = BAcos(theta)

need help, can't find a correct answer.

 

[anathema]

Hello, thank you for your post. I am a scientist and I can help you with this problem.

First, let's start by identifying the given information:

- Area (A) = 0.028 m2
- Magnetic field (B) = 2.0 T
- Normal (θ) = parallel to magnetic field
- Average induced emf (E) = 0.010 V

We can use the formula E = -N * ΔΦ/Δt, where N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time.

We also know that magnetic flux (Φ) is equal to BAcos(θ), where B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the normal.

Now, let's plug in the given values and solve for Δt:

0.010 V = -N * (2.0 T) * (0.028 m2) * cos(0°)/Δt

0.010 V = -N * (0.056 Tm2)/Δt

-0.010 V/(-0.056 Tm2) = N/Δt

0.179 s = N/Δt

Therefore, the smallest time period during which the field can be allowed to vanish is 0.179 s. This means that if the magnetic field is shut off suddenly, it must be restored within 0.179 seconds to keep the induced emf below 0.010 V.

I hope this helps. Let me know if you have any further questions.

 

[Moetasim]

I understand your frustration with not being able to find a correct answer for this question. It seems like you have the right formulas and approach, but perhaps there is an error in your calculations. I would suggest double-checking your calculations and make sure you are using the correct units for each variable. It is also important to consider the direction of the induced emf and whether it will add or subtract from the existing magnetic field.

Additionally, it may be helpful to break down the problem into smaller steps and solve for each variable separately. For example, first solve for the induced emf, then use that value to calculate the time period. This can help identify any errors in your calculations.

If you are still having trouble, I recommend seeking help from a colleague or professor who may be able to offer additional guidance. It is also important to remember that in real-life situations, there are many factors at play and it may not be possible to calculate an exact answer. In this case, it would be important to consider the safety precautions and protocols in place to minimize the impact of any equipment failure on the patient.