# Tutor profile: Elena L.

## Questions

### Subject: Physics (Electricity and Magnetism)

What is the quasi-static approximation?

While at high frequencies the electric and magnetic field are always coupled, as described by Maxwell’s equations, at the low frequency range a quasi-static approximation can be used. Such approximation consists on decoupling the E and H-field, because the dimensions of the exposed body are electrically small compared to the field wavelength. Specifically the approximations are strictly related to the dimensions of the exposed object with respect to the incident wave. In the static or quasi-static state (ω → 0), the E and H fields are completely decoupled, and therefore can be solved independently. For static field Maxwell’s equation are heavily simplified into decoupled electrostatic and magnetostatic equations. Conversely, in quasi-static state only one of the two time derivative becomes important for the calculation depending on the relative importance of the two dynamic coupling terms. The Quasi-static approximation implies that the field at a given time are determined indipendently on what the sources of the field were at an earlier time, because the process under consideration is much slower than the propagation time of an electromagnetic wave . Hence, quasistatics approxi- mation assumes that the field strengths change so slowly in time (quasistatic) that the E and H fields induced by those changes (the contributions to E and H from the ∂/∂t terms in Maxwell’s equations) are sufficiently small, and by consequence the induced fields (∝ (∂/∂t)^2) can be neglected (i.e., fields are decoupled); only the original and first-order induced fields are therefore of interest.

### Subject: Biomedical Science

Is MRI dangerous for patients?

The attention to patient safety started as soon as the first MR images of humans were produced. The power of MRI is the use of non-ionising radiation. This is the main safety advantage of this diagnostic tool in contrast with the use of X-ray. However, although MRI is overall safe technology, there are possible risks to the patients. The risks associated with the MRI are related to the electromagnetic fields produced by the system to generate the radiological image. To generate the final image, the MRI system uses three magnetic field typologies: a static field, a time-varying radio frequency field, and a spacial varying gradient field. While the static filed, in the MRI context, was proven to produce no effects on biologic tissues, radiofrequency and gradient fields can generate some kind of harmful bioeffect to the patient. The gradients field are able to stimulate the patient's nerves and muscles, and patient sensation can be “tingling” or “tapping”. Conversely, radiofrequency fields are able to heat up biological tissues, thus localized high temperature can be experienced by the patient. These bioeffects related to gradient and radiofrequency field are due to the interaction of the patient body with these specific typologies of magnetic field. In fact, it is known that in a conductive medium (such as the human body) a time or space varying magnetic field generates a time or space varying electric field. The generated electric field is the main responsible of these bioeffects. However there is nothing to worry about because international standards are available to assess safety of patients undergoing an MRI scan. The standards report limits and test methods, and they define the procedures to be follow to assure and assess safety conditions. Within the standards special references can be found for patient not in normal conditions, such as infants, pregnant women, and people with impaired thermoregulatory ability as a result of age, disease or the use of medications.

### Subject: Algebra

How can I use the scientific notation to find an easy solution to the apparently complicated operation: 0.00015 * 5372 / 15?

The scientific notation allows to express numbers using a decimal form. For the specific case reported the scientific notation can be very useful to quickly solve the operation. In fact, the expression can be written as: (1.5 * 10^-4 * 5.372 * 10^3) /( 1.5 * 10) we can now group all the coefficients and decimals together, thus the expression becomes: (1.5*5.372/1.5)*(10^-4*10^3 / 10) The first part of the expression can be easily solved because the 1.5 can be simplified as present both at the numerator and denominator. Whereas the second part of the expression can be solved using the properties of the exponents. Hence, the expression becomes (already simplifying 1.5 in the first part): 5.372 * 10^(-4+3-1) Please notice that the 10 at the denominator was brought to the nominator as 10^-1. The final solution of the operation is 5.372*10^-2 that can now be converted back to its decimal notation: 0.05372

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