Current Density is the measurement of electric current (charge flow in amperes) per unit area of cross-section (m²). This is a vector quantity, with both a magnitude (scalar) and a direction.

J = I/A

J = current density in amperes/m²

I = current through a conductor, in amperes

A = cross-sectional area of the conductor, m²

Current Density Formula example:

A current of 6 mA is flowing through a copper wire that has an area of 4 mm². What is the current density?

Answer: The current through the conductor is I = 6 mA = 0.006 amperes (or 6 x 10^-3 amps). The area of the wire is A = 4 mm² = 0.004 m² (or 4 x 10^-3 m²). Use the equation for current density.

J = I/A

J = 0.006 amps/0.004 m²

J = 1.5 amps/m²

Current density and Ohm's law

The current density (current per unit area) J → {\displaystyle {\vec {J}}} J  in materials with finite resistance is directly proportional to the electric field E → {\displaystyle {\vec {E}}} E in the medium. The proportionality constant is called the conductivity σ {\displaystyle \sigma } of the material (measured in siemens/m), whose value depends on the material concerned and, in general, is dependent on the temperature of the material:

J → = σ E → {\displaystyle {\vec {J}}=\sigma {\vec {E}}\,} J = E

This equation is the Ohm's Law (V=IR), here in this equation the current density is which relates voltage, current and resistance that is the E (electric field) is analogous to voltage, current density (J) is analogous to current, and the conductivity is the inverse of resistance. This is where Ohm's Law for circuits comes from.

The reciprocal of the conductivity σ {\displaystyle \sigma } of the material is called the electrical resistivity ρ {\displaystyle \rho } of the material and the above equation, when written in terms of resistivity becomes:

J → = E → ρ {\displaystyle {\vec {J}}={\frac {\vec {E}}{\rho }}} J = E /  

or

E → = ρ J → {\displaystyle {\vec {E}}=\rho {\vec {J}}} E = J

In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform. In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal) resistor (or other ohmic device):

I = V R , {\displaystyle I={V \over R}\,,}

where I {\displaystyle I} is the current, measured in amperes; V {\displaystyle V} is the potential difference, measured in volts; and R {\displaystyle R} is the resistance, measured in ohms.

For alternating currents, especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.

Electrosurgery is based on heat effect of the current and this propotional to the tissue conductivity and the square of the current density (the electric field). The power volume density Wv falls extremely rapidly with distance from the electrode as given by the formula below

Wv = i² / 4 π² σ r⁴

Tissue destruction therefore occurs in very vicinity of the electrode. Power dissipation is linked with conductance and not admittance.

Tissue Temperature Generated  =

Temp. = (I^r/r⁴) x R x t

I = current

r = radius of tissue or conductor

t = time

since radius is getting multiplied to the power 4, therefore small changes int he diameter result in large changes in heat generated. Heat is also linked with the rms values of the voltage and current.

RMS voltage -( root mean squared voltage)

RMS voltage value of a sinusoidal waveform gives the same heating effect as an equivalent DC (direct current) power.

For a sine wave, the RMS value is 0.707 times the peak value or 0.354 times the peak to peak value.

for example AC voltmeters show RMS value of the voltage or current

therefore 230 volts RMS = 0.707 x peak rate of voltage

          or peak value of voltage = 230 / 0.707 = 325 volts

another way to calculate the peak voltage is by mulitplying RMS voltage with √2

       = 230 x √2

       = 230 x 1.414 = 325.22 volts.

Typical power levels used in electrosurgery are

Unipolar surgery - 80 Watts (500 Ω, 200 V, 400 mA rms)

Bipolar surgery - 15 Watts ( 100 Ω, 40 V, 400 mA rms)

in pulsed mode of unipolar electrosurgery, the peak voltage can reach 5000V

Electrical current for medical purposes operates at frequencies of 240 KHz to 3.3 MHz that is above the range where neuro-muscular stimulation or electrocution cannot occur.

Short circuit

A short circuit is an electric circuit offering little or no resistance to the flow of current. Short circuits are dangerous with high voltage power sources because the high currents encountered can cause large amounts of heat energy to be released. The current in an electrical device is directly proportional to the electric potential difference impressed across the device and inversely proportional to the resistance of the device. 

Electrical power was defined as the rate at which electrical energy is supplied to a circuit or consumed by a load. The equation for calculating the power delivered to the circuit or consumed by a load was derived to be

P = V  I (Power = Voltage x current)

and as per Ohm's Law

V = IR

or

I = V/R

Therefore power is also calculated as

P = V²/R    or     P = I²R

To illustrate, suppose that you were asked this question: If a 60-watt bulb in a household lamp was replaced with a 120-watt bulb, then how many times greater would the current be in that lamp circuit?

Using the above equations, one might reason (incorrectly), that the doubling of the power means that the I² quantity must be doubled. Thus, current would have to increase by a factor of 1.41 (the square root of 2). This is an example of incorrect reasoning because it removes the mathematical formula from the context of electric circuits. The fundamental difference between a 60-Watt bulb and a 120-Watt bulb is not the current that is in the bulb, but rather the resistance of the bulb. It is the resistances that are different for these two bulbs; the difference in current is merely the consequence of this difference in resistance. If the bulbs are in a lamp socket that is plugged into a outlet, then one can be certain that the electric potential difference is around 120 Volts. The ΔV would be the same for each bulb. The 120-Watt bulb has the lower resistance; and using Ohm's law, one would expect it also has the higher current. In fact, the 120-Watt bulb would have a current of 1 Amp and a resistance of 120 Ω; the 60-Watt bulb would have a current of 0.5 Amp and a resistance of 240 Ω.

 Now calculating for the current flow between the two bulbs

Terminology used in electrosurgery

The word cautery originates from the latin, meaning to brand. It relates to the coagulation or destruction of tissue by heat or a caustic substance.

Electrosurgery (particularly electrocoagulation) is sometimes incorrectly called diathermy, which means ‘dielectrical heat’. Diathermy is produced by rotation of molecular dipoles in high frequency alternating electric field – the effect produced by a microwave oven.

Electrosurgery includes:

• Electrofulguration (results in sparks)

• Electrodesiccation (dehydration of superficial tissue)

• Electrocoagulation (cause bleeding blood vessels to clot)

• Electrosection (cut through tissue)

• Thermocautery

• Radiofrequency devices (very high frequency, for cutting [>1,500kHz])

Electrosurgery may be monoterminal, monopolar or bipolar.

Monoterminal electrosurgery

• Handpiece has single electrode.

• Indifferent electrode is not required.

Monopolar electrosurgery

• Uses single pointed probe to carry electrical current from power generator to surgical site.

• Requires indifferent electrode, typically large metal plate or flexible metalised plastic pad placed on skin distant from surgical site.

• Current passes from tip of probe through patient to indifferent electrode and completes circuit by returning to electrosurgical generator.

Bipolar electrosurgery

• Uses forceps with both tines connected to power generator: one is active and other is indifferent electrode.

• Current runs through tissue grasped by forceps.

• Used in patients with implanted cardiac devices such as a pacemaker or defibrillator, to prevent electrical current passing through the device, which might short-circuit or fire inappropriately.

Waveforms in electrosurgery

Different waveforms may be generated by the electrosurgery machine for different procedures.

• Continuous single, high frequency (>400 V) sine wave used at high heat for cutting / vaporisation leaves a zone of thermal damage. A high pitched sound is heard.

• Pulsed or modulated waveforms allow tissue to cool between bursts so that the zone of thermal damage is minimal.

• A sine wave turned on and off in a rapid succession (rectified) produces the slower heating process that results in coagulation. A rougher, lower tone is heard due to lower power.

• Variable waveforms can be produced to blend cut and coagulation, as power is adjusted in real time depending on tissue impedance.

Electrofulguration and electrodessiccation

Electrofulguration and electrodesiccation are used to destroy superficial lesions that are unlikely to bleed profusely when disturbed, such as viral warts and seborrhoeic keratoses.

Electrofulguration and electrodesiccation use a single electrode to produce high voltage and low amperage current. The current accumulates in the patient but there is minimal tissue damage.

Electrofulguration

• Electrofulguration is used to treat skin tags and protruding warty lesions such as seborrhoeic keratoses, viral warts, xanthelasma and dermatosis papulosa nigra.

• Electrode is held 1–2 mm from skin surface, and produces spark or electric arc.

• This causes superficial tissue dehydration and carbonisation over wide area.

• High voltage allows current to overcome resistance of air gap between tissue and electrode tip.

• Carbonised epidermis insulates and minimises further damage to the underlying dermis.

Electrodesiccation

• Electrodesiccation is used to remove flat seborrhoeic keratoses and lesions under the skin such as syringoma, milia, comedones, sebaceous hyperplasia and molluscum contagiosum.

• It can be also used for hair removal and to treat fine facial blood vessels.

• Electrode contacts skin directly and heats it up

• Results in dehydration of surface and slightly deeper skin

• Dry coagulum forms on skin surface.

• Treated areas usually heal rapidly with minimal scarring or loss of pigment

The Conmed Hyfrecator is a brand name for a low-powered electrosurgical device used for electrofulguration, electrodessication and electrocoagulation. The term ‘hyfrecation’ is often used generically to describe similar devices made by other manufacturers. The power output is adjustable, and the pencil handpiece may be equipped with different stainless steel tips, including the following types.

• Sharp straight and angle tipped needle electrodes of varying length and diameter are used for pin-point haemostasis and hair removal.

• Blade shaped blunt tipped electrode is used for incisions.

• Blunt tips and ball tips are used for electodessication and electrocoagulation.

• Adapters can be used with hypodermic needles to treat very fine telangiectasias

• Bipolar forceps are used for precise coagulation or to grip pedunculated lesions and may have micro tips, smooth or serrated tips.

• Disposable tips reduce chance of transmitting microbial infection and can be replaced when eschar builds up.

• Tips coated with Teflon (polytetrafluoroethylene or PTFE) or elastomeric silicone reduce eschar build-up and can be wiped

Electrocoagulation

Electrocoagulation is used to cause deeper tissue destruction and to stop bleeding with minimal carbonisation. The haemostatic and destructive capacity of electrocoagulation makes it ideal for the treatment of skin cancers and vascular skin conditions such as pyogenic granuloma. It can also be used to stop small blood vessels from bleeding during skin surgery.

Electrocoagulation uses monopolar or bipolar electrodes to produce low voltage and high-amperage current at relatively low power. An indifferent electrode prevents accumulation of current in the patient, hence low voltage is sufficient to establish current flow. High amperage causes deep tissue destruction and haemostasis by fusion of blood vessel collagen and elastic fibres.

The electrode is applied across the lesion until slightly pink to pale coagulation occurs. Coagulated tissue has greater resistance to electrical current than normal skin, and limits the amount of damage.

Electrocoagulation may result in permanent scarring and white marks (hypopigmentation).

Electrosection

Electrosection is used to simultaneously cut skin and seal bleeding vessels by blending damped and undamped wavetrains. It is suited for excision of large, relatively vascular lesions, such as benign dermal naevi (moles), skin tags, or for shaving off seborrhoeic keratoses, folliculitis keloidalis nuchae and rhinophyma (see rosacea). Electrosection requires almost no manual pressure from the operator as the electrode glides through tissue with minimal resistance.

Electrosection uses an monopolar electrode to produce low-voltage and high-amperage current at higher power than is used for electrocoagulation. The current is highly focused to vaporise tissue with minimal peripheral heat damage. The electrode is usually a fine tungsten wire or loop.

The destruction of chemical bonds or decomposition of tissue arises through thermolysis (heat-induced) and electrolysis (via DC electric-current). The main component of tissue is water, which is broken down into its components, hydrogen and oxygen.

Radiofrequency devices are often used for electrosection. They produce little heat so cause little collateral tissue damage.

Compared with surgical removal, benefits of electrosection include reduced surgical time, reduced post-operative complications (pain, swelling, infection), maximum readability of histologic specimen, enhanced healing and excellent cosmetic results. No sutures are necessary when it is used to remove small skin lesions flush with the normal skin contour.

Thermocautery

The term electrocautery is most often used in reference to a device in which a direct current is used to heat the cautery probe. As no current flows through the patient, this is not a true form of electrosurgery. It is therefore preferable to use the term thermocautery for these devices.

Thermocautery is used for pinpoint haemostasis during surgical procedures or to get rid of small blood vessels (telangiectasias).

Direct electric current is used to heat the surgical element, which then causes thermal injury by direct heat transference to the tissue. In contrast, in electrosurgery, the treating electrode remains cold.

Portable and disposable thermocautery devices are available powered by penlight batteries. The Shaw Hemostatix® Scalpel is a form of thermocautery in which a heated disposable copper alloy blade is used to cut tissue with reduced bleeding in highly vascular areas.

Thermocautery is suitable for patients with an implanted pacemaker or defibrillator.

Risks of electrosurgery

The risks of electrosurgery include electric shock and electrical burns, thermal burns, transmission of infection and production of toxic gases.

Electric shock

Electric/thermal burns

Electric/thermal burns can be minimised by:

Transmission of infection and production of toxic gases

Electrosurgery may be used to treat viral warts. Thermolysis will generate smoke/fumes which may contain human papillomavirus (HPV) particles that may be transmitted to the operator who breaths in or comes into contact with the fume. When working with HPV-related lesions, minimise the risk of transmission.

• Use smoke evacuator with intake nozzle 2 cm from operative site

• Wear surgical mask (N95 is most effective) and eye protection.

Other viral DNA, bacteria, carcinogens, and irritants are also known to be present in electrosurgical smoke. NIOSH (the National Institute of Occupational Safety and Health) a division of CDC (Center for Disease Control, USA) have also studied electrosurgical smoke at length. They state: “Research studies have confirmed that this smoke plume can contain toxic gases and vapors such as benzene, hydrogen cyanide, and formaldehyde, bioaerosols, dead and live cellular material (including blood fragments), and viruses.”

Smoke can be removed using hand held suction. Newer smoke evacuation devices can be attached directly to a standard electrosurgical pencil reducing the work of an assistant during surgery.

Cardiac pacemaker and defibrillators

Electric currents from electrosurgery electrodes pass through the patient's body to the indifferent electrode. This may sometimes cause malfunction of implanted cardiac devices.

This risk may be mitigated in the following ways.

• Use thermocautery including Shaw scalpel (no current flow through patient)

• Use bipolar forceps with electrosurgery device (minimises current through patient)

• If possible, avoid operating near the implanted device

• Change pacemaker to fixed-rate mode or magnetically deactivate implantable cardioverter-defibrillator during electrosurgery.