] Electrostatic potential energy stored in a configuration of discrete point charges

The mutual electrostatic potential energy of two charges is equal to the potential energy of one charge in the electrostatic potential generated by the other. That is to say, if charge q1 generates an electrostatic potential \Phi_1(\mathbf r), which is a function of position \mathbf r, then U_E = q_2 \Phi_1(\mathbf r_2). Also, a similar development gives U_E = q_1 \Phi_2(\mathbf r_1).

This can be generalized to give an expression for a group of N charges, qi at positions \mathbf r_i:

U_E = \frac{1}{2}\sum_i^N q_i \Phi(\mathbf r_i)

where, for each i value, \Phi(\mathbf r_i) is the electrostatic potential due to all point charges except the one at \mathbf r_i

Note: The factor of one half accounts for the 'double counting' of charge pairs. For example, consider the case of just two charges.

Alternatively, the factor of one half may be dropped if the sum is only performed once per charge pair. This is done in the examples below to cut down on the math.
One point charge

The electrostatic potential energy of a system containing only one point charge is zero, as no work is required to move the charged particle from infinity to its location.
Two point charges

Consider bringing a second point charge into position. The electrostatic potential Φ(r1) due to charge 1 is

\Phi(r_1) = \; k_{\mathrm{e}} q_1/r_1
where ke is Coulomb's constant. In the International System of Quantities, which has been the preferred international system since the 1970s and forms the basis for the definition of SI units, the Coulomb constant is given by

k_{\mathrm{e}} = \; 1/4 \pi \epsilon_0 ,

where ε0 is the electric constant. Hence we obtain:

U_\mathrm{E} = \; \frac{q_1 q_2}{4 \pi \epsilon_0 r}

where

q1, q2 are the two charges
r is the distance between the two charges

The electrostatic potential energy will be negative if the charges have opposite sign and positive if the charges have the same sign. Negative mutual potential energy corresponds to attraction between two charges; positive mutual potential energy to repulsion between two charges
Three or more point charges

For 3 or more point charges, the electrostatic potential energy of the system may be calculated by bringing individual charges into position one after another, and taking the sum of the energies required to bring each additional charge into position. Thus

U_\mathrm{E} = \frac{1}{4 \pi \epsilon_0} \left({\frac{q_1 q_2}{r_{12}}} + {\frac{q_1 q_3}{r_{13}}} + {\frac{q_2 q_3}{r_{23}}} + ...\right)

where

q1, q2, ..., are the point charges
rmn is the distance between two point charges, m and n (e.g. r12

Electric potential energy

Electric potential energy (also known as "electrostatic potential energy") is a potential energy associated with the conservative Coulomb forces within a defined system of point charges. The term "electrostatic potential energy" is preferred here because it seems less likely to be misunderstood. The reference zero is usually taken to be a state in which the individual point charges are very well separated ("are at infinite separation") and are at rest. [1]:§25-1 The electrostatic potential energy of the system (UE), relative to this zero, is equal to the total work W that must be done by a hypothetical external agent in order to bring the charges slowly, one by one, from infinite separation to the desired system configuration:

U_{\mathrm{E}} = \; W \;.

In this process the external agent is deemed to provide or absorb any relevant work, and the point charge being slowly moved gains no kinetic energy.

Sometimes people refer to the potential energy of a charge in an electrostatic field. This actually refers to the potential energy of the system containing the charge and the other charges that created the electrostatic field.[1]:§25-1

To calculate the work required to bring a point charge into the vicinity of other (stationary) point charges, it is sufficient to know only (a) the total field generated by the other charges and (b) the charge of the point charge being moved. The field due to the charge being moved and the values of the other charges do not need to be known. Nonetheless, in many circumstances it is mathematically easier to add up all the pairwise potential energies (as below).

It is important to understand that electrostatics is a 18th-19th-century theory of hypothetical entities called "point charges". Electrostatics is categorically not a complete theory of the charged physical particles that make up the physical world, and are subject to the Heisenberg uncertainty principle and other laws of quantum mechanics

analytica

Longwave (Kilohertz) Ultrasound

Ultrasound, as a therapy, involves the application of sound energy at a frequency above the normal hearing range (approximately 16Hz - 20,000 Hz). Mechanical energy beyond this range is not audible, though the nature of the energy does not change – it is still a mechanical (pressure) wave. Therapeutic Ultrasound frequencies usually between 1 and 3 MHz (millions of cycles per second) whereas Longwave ultrasound in the 40 – 50 kHz range (tens of thousands of cycles per second). Whilst this is clearly still beyond the normal upper limit for audible sound, it is not as far removed as traditional (MHz) ultrasound. It is probably preferable to refer to this particular form of ultrasound therapy as kilohertz ultrasound (as a way to distinguish it from the more normal MHz (Megahertz) ultrasound therapy. For additional information relating to the ‘physics’ of ultrasound, the basic ultrasound page/handout should have the basic information that you need.

It is suggested that due to its lower frequency and therefore greater wavelength, the energy will penetrate further into the tissues and thus ‘reach’ deeper tissues and have effects that traditional ultrasound is unable to achieve. This may or may not in fact be the case, and the biggest problem lies with the lack of specific research into ‘longwave’ or ‘kiloherts’ ultrasound.
One of the major effects of this different frequency is that there is claimed to be a difference in the effective penetration depth. By employing a LOWER FREQUENCY, the wavelength will be greater (assuming the velocity in tissue is approximately constant). The relationship between sound wave frequency, tissue velocity and wavelength is denoted thus :
v = f.l
At 3MHz, the wavelength (l) will be in the order of 0.5mm
At 1MHz the wavelength will be in the order of 1.5mm
At 45kHz the wavelength will be in the order of several 10’s of cm’s (around 30cm at 45kHz)
The effective penetration depth is also related to frequency. It is known that 1MHz and 3MHz are absorbed at different rates in the tissues and therefore have different penetration depths. The penetration depth of kilohertz US is expected to be in excess of 20 times greater than MHz ultrasound.

Galvanic Stimulation (GS)

Galvanic stimulation is most useful in acute injuries associated with major tissue trauma with bleeding or swelling. In contrast to TENS and IFC units, which apply alternating current, galvanic stimulators apply direct current.
Direct current creates an electrical field over the treated area that, theoretically, changes blood flow. The positive pad behaves like ice, causing reduced circulation to the area under the pad and reduction in swelling. The negative pad behaves like heat, causing increased circulation, reportedly speeding healing.

Interferential Current (IFC)

Interferential current is essentially a deeper form of TENS. In essence, IFC modulates a high frequency (4000 Hz) carrier waveform with the same signal produced by a TENS unit. The high frequency carrier waveform penetrates the skin more deeply than a regular TENS unit, with less user discomfort for a given level of stimulation. Deep in the tissues, the carrier waveform is cancelled out, resulting in a TENS-like signal deep under the skin.
Anecdotal evidence suggests that the IFC units may be useful for patients who have not had relief from TENS. However, at $2000 per unit, IFC devices are significantly more expensive than TENS units.

Transcutaneous Electrical Nerve Stimulators (TENS)

The patient may use a TENS unit at home for back pain relief on a long-term basis. TENS units are about the size of a pack of cigarettes and typically cost $250 - $700. All units allow the user to adjust the intensity of the stimulation; some units also allow the user to select high-frequency stimulation (60 - 200 Hz) or low-frequency stimulation (<10 Hz).
High frequency stimulation, sometimes called "conventional", is tolerable for hours, but the resultant pain relief lasts for a shorter period of time. Low-frequency stimulation, sometimes called "acupuncture-like", is more uncomfortable and tolerable for only 20-30 minutes, but the resultant pain relief lasts longer.

TENS users should experiment with various electrode placements. Electrodes can be placed over the painful area, surrounding the painful area, over the nerve supplying the painful area, or even on the opposite side of the body. TENS users need to try the unit for several days with several electrode placements prior to deciding if it will be useful. A home trial for several days to weeks is preferable.

Common characteristics of electrotherapy stimulation

TENS, IFC, and GS all apply electrical stimulation to nerves and muscles via adhesive pads placed on the skin. These devices are powered by batteries, and some units have an adapter that allows powering from an outlet.

Side effects are rare, but include allergic skin irritation under the adhesive pads and transient pain from the electrical charge. Placing the pads over the heart or over pacemaker leads could conceivably cause cardiac arrhythmia; placing them over the throat could conceivably cause low blood pressure; and placing them over a pregnant uterus could conceivably cause fetal damage. Because of these risks, electrical stimulation over these areas should be avoided. Electrical stimulation should also not be applied over malignancies or infected areas.

what is electrotherapy

Electricity has been used to treat pain for over 100 years. Early proponents of electricity were labeled as charlatans, but recent scientific studies have proven that electricity can reduce both acute and chronic pain.
In This Article:

* Electrotherapy
* Transcutaneous Electrical Nerve Stimulators (TENS)
* Interferential Current (IFC)
* Galvanic Stimulation (GS)

The exact mechanism of electrical stimulation’s beneficial effect remains controversial. Electrical stimulation may directly block transmission of pain signals along nerves. In addition, electrical stimulation has been shown to promote the release of endorphins, which are natural painkillers produced by the body.

Several different electrical stimulation devices exist, each producing different frequencies, waveforms, and effects. Electrical modalities include

*

Transcutaneous Electrical Nerve Stimulation (TENS) (the most commonly used)
*

Interferential Current (IFC)
*

Galvanic Stimulation (GS)

cancer

Carcinogenesis is a dangerous if long exposure to UVB or UVC occurs, as these rays may have an effect on DNA and thus on cell replication. the evidence supporting the hypothesis that skin cancer is produced by ultra-violet radiation is considerable, so prolonged exposure of the patient's skin to the shorter ultra-violet waves should be avoided and courses of treatment should not exceed four weeks.

PHYSIOLOGICAL EFFECTS OF ULTRA-VIOLET

the skin acts as a protective layer, in that it absorbs most ultra-violet light and prevents its penetration down to vulnerable cells. if ultra-violet waves are absorbed by the skin, the energy they release is sufficient to cause damages, and the consequent reaction, depends upon the wavelength of ultra-violet and the amount of ultra-violet absorbed. UVC and UVB are absorbed in the epidermis, but UVA may penetrate as far as the capillary loops in the dermis .

ELECTROMYOGRAPHY

Recording is made through of those aspects of electromyography

ELECTRODIAGNOSIS

changes in electricla reactions
When there is disease orinjury of motor nerves or muscles, alterations are liable to occur in thier response to electrical stimulation. the altered electrical reactions may be of considerable assistance in diagnoing the type and extent of the lesion.
Reduction or loss of voluntary power of a muscle may be due to:

1. a lesion of the upper motor neurone.
2. a lesion of the upper motor neurone.
3. damage to the muscle itself.
4. A fault at the neuromuscular junction
5. A functional disorder.

the parts of the motor pathway which are normally accessible for electrical stimulation are the lower motor neurone below its exits from the vertebral canal and the muscle itself, but not the anterior horn cell or the upper motor neurone

current use

Although a 1999 meta-analysis found that electrotherapy could speed the healing of wounds, in 2000 the Dutch Medical Council found that although it was widely used, there was insufficient evidence for its benefits. Since that time, a few publications have emerged that seem to support its efficacy, but data is still scarce.

The use of electrotherapy has been widely researched and the advantages have been well accepted in the field of rehabilitation (electrical muscle stimulation). The American Physical Therapy Association acknowledges the use of Electrotherapy for: 1. Pain management Improve range of joint movement 2. Treatment of neuromuscular dysfunction Improvement of strength Improvement of motor control Retard muscle atrophy Improve local blood flow 3. Improve range of joint mobility Induce repeated stretching of contracted, shortened soft tissues 4. Tissue repair Enhance microcirculation and protein synthesis to heal wounds Restore integrity of connective and dermal tissues 5. Acute and chronic edema Accelerate absorption rate Affect blood vessel permeability Increase mobility of proteins, blood cells and lymphatic flow 6. Peripheral blood flow Induce arterial, venous and lymphatic flow 7. Iontophoresis Delivery of pharmacological agents 8. Urine and fecal incontinence Affect pelvic floor musculature to reduce pelvic pain and strengthen musculature Treatment may lead to complete continence

Electrotherapy is used for relaxation of muscle spasms, prevention and retardation of disuse atrophy, increase of local blood circulation, muscle rehabilitation and re-education electrical muscle stimulation, maintaining and increasing range of motion, management of chronic and intractable pain, post-traumatic acute pain, post surgical acute pain, immediate post-surgical stimulation of muscles to prevent venous thrombosis, wound healing and drug delivery.

Reputable medical and therapy Journals have published peer-reviewed research articles that attest to the medical properties of the various electro therapies. Yet some of the treatment effectiveness mechanisms are little understood. Therefore effectiveness and best practices for their use in some instances are still anecdotal.

Electrotherapy devices have been studied in the treatment of chronic wounds and pressure ulcers. A 1999 meta-analysis of published trials found some evidence that electrotherapy could speed the healing of such wounds, though it was unclear which devices were most effective and which types of wounds were most likely to benefit.However, a more detailed review by the Cochrane Library found no evidence that electromagnetic therapy, a subset of electrotherapy, was effective in healing pressure ulcers or venous stasis ulcer

use of eletrotherapy

In 1855 Guillaume Duchenne, the father of electrotherapy, announced that alternating was superior to direct current for electrotherapeutic triggering of muscle contractions. What he called the 'warming affect' of direct currents irritated the skin, since, at voltage strengths needed for muscle contractions, they cause the skin to blister (at the anode) and pit (at the cathode). Furthermore, with DC each contraction requiring the current to be stopped and restarted. Moreover alternating current could produce strong muscle contractions regardless of the condition of the muscle, whereas DC-induced contractions were strong if the muscle was strong, and weak if the muscle was weak.

Since that time almost all rehabilitation involving muscle contraction has been done with a symmetrical rectangular biphasic waveform. In the 1940s, however, the US War Department, investigating the application of electrical stimulation not just to retard and prevent atrophy but to restore muscle mass and strength, employed what was termed galvanic exercise on the atrophied hands of patients who had an ulnar nerve lesion from surgery upon a wound. These Galvanic exercises employed a monophasic wave form, direct current - electrochemistry.