# Magnetic field effects in high-power batteries; 1: The penetration of an electric field into a cylindrical conductor

## Abstract

The penetration of the axial component of an electric field into a cylindrical conductor is described by an asymptotic solution method for long and short times. The development of the respective current distributions allows for a mathematical comparison of the solution schemes and indicates that the current initially increases at a rate proportional to time until a time of order [epsilon]/[sigma], subsequently at a rate proportional to the square root of time, and finally levels off exponentially to the steady-state value. Numerical estimates of these time frames for a bipolar lead-acid battery with porous lead electrodes of 0.10 m radius give values of 1 [times] 10[sup [minus]18] s for the inner time regime and 0.1 s for the diffusion time regime. Criteria for the proper omission of the displacement current also are given.

- Authors:

- (Univ. of California, Berkeley, CA (United States). Materials Sciences Div.)

- Publication Date:

- OSTI Identifier:
- 7110014

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Journal Name:
- Journal of the Electrochemical Society; (United States)

- Additional Journal Information:
- Journal Volume: 141:3; Journal ID: ISSN 0013-4651

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 25 ENERGY STORAGE; LEAD-ACID BATTERIES; DESIGN; INDUCTANCE; ELECTRIC FIELDS; MAGNETIC FIELDS; MATHEMATICAL MODELS; PERFORMANCE; TIME DEPENDENCE; VOLTAGE DROP; ELECTRIC BATTERIES; ELECTRICAL PROPERTIES; ELECTROCHEMICAL CELLS; PHYSICAL PROPERTIES; 250901* - Energy Storage- Batteries- Design & Development; 250902 - Energy Storage- Batteries- Performance & Testing

### Citation Formats

```
Battaglia, V., and Newman, J..
```*Magnetic field effects in high-power batteries; 1: The penetration of an electric field into a cylindrical conductor*. United States: N. p., 1994.
Web. doi:10.1149/1.2054795.

```
Battaglia, V., & Newman, J..
```*Magnetic field effects in high-power batteries; 1: The penetration of an electric field into a cylindrical conductor*. United States. doi:10.1149/1.2054795.

```
Battaglia, V., and Newman, J.. Tue .
"Magnetic field effects in high-power batteries; 1: The penetration of an electric field into a cylindrical conductor". United States. doi:10.1149/1.2054795.
```

```
@article{osti_7110014,
```

title = {Magnetic field effects in high-power batteries; 1: The penetration of an electric field into a cylindrical conductor},

author = {Battaglia, V. and Newman, J.},

abstractNote = {The penetration of the axial component of an electric field into a cylindrical conductor is described by an asymptotic solution method for long and short times. The development of the respective current distributions allows for a mathematical comparison of the solution schemes and indicates that the current initially increases at a rate proportional to time until a time of order [epsilon]/[sigma], subsequently at a rate proportional to the square root of time, and finally levels off exponentially to the steady-state value. Numerical estimates of these time frames for a bipolar lead-acid battery with porous lead electrodes of 0.10 m radius give values of 1 [times] 10[sup [minus]18] s for the inner time regime and 0.1 s for the diffusion time regime. Criteria for the proper omission of the displacement current also are given.},

doi = {10.1149/1.2054795},

journal = {Journal of the Electrochemical Society; (United States)},

issn = {0013-4651},

number = ,

volume = 141:3,

place = {United States},

year = {1994},

month = {3}

}