### Accident or Abuse?

Written by Barbara A. Williams

Police officers were called by officials at the Christiana Hospital in Delaware to investigate a possible case of child abuse. All injuries to children are now investigated by local authorities who are concerned about protecting children from subsequent incidents of child abuse. The following statement was made by a babysitter who brought the unconscious young child to the emergency room.

"Thomas was crawling around on the rug and playing with his toys. When he reached for a large metal truck, a prominent spark lasting 5 msec appeared between his fingertip and the object. His fingertip was about 2 mm from his toy truck when the spark appeared. After the flash, Thomas collapsed. I saw his burnt finger, and fearing a severe injury due to the spark, I rushed him to the emergency room".

The investigator understands currents as large as 0.001 amp produce a harmless mild tingling sensation at the point of contact. Currents in 0.01 - 0.02 amp range can cause muscle spasms. Any above 0.2 amp can be potentially fatal. On the day of the accident, the weather was cold and dry. Under these conditions, the air would have become conducting when the electric field reached 3 x 106 N/C. The investigator checks the hospital records and notes that the burned region on the child's fingertip is 10-4 m2.

• Is it possible for the child to become electrically charged based on the babysitter's statement? Explain using physics principles.
• Draw the child's fingertip and the region of the toy truck just before the spark appeared. Show the approximate charge distribution on both. Explain in words your diagram. (Assume that the truck is neutral.)
• Explain in words how you would determine the charge on the child's fingertip.
• Would the electric interaction described by the babysitter be harmful to the child? (Give a detailed quantitative explanation.)
• Estimate the resistance of the dry air between the toy truck and the child's fingertip. Is your estimate consistent with what you would have expected before making any of the previous calculations?
• Is there reason for the investigator to suspect foul play when she compares the babysitter's version of the incident and the conclusions she reaches after having applied physics principles to the problem? Explain.

 "http://www.udel.edu/pbl/curric/phys202exam1.html" Last updated Nov. 22, 1996. Copyright Barbara Williams, Univ. of Delaware, 1996.