An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem asks for the formula of electric field strength E.
The correct formula is E = d 2 k q .
Among the options, E = a 2 ka is the closest if we consider a as the distance and assume q = 1 .
Therefore, the answer is E = a 2 ka .
Explanation
Understanding the Problem We are asked to identify the correct formula for the electric field strength ( E ) at a distance from a known source charge. The electric field is a vector field that represents the electric force exerted on a test charge at a given point.
Recalling Coulomb's Law The electric field ( E ) due to a point charge ( q ) at a distance ( d ) is given by Coulomb's Law for the electric field: E = d 2 k q , where k is Coulomb's constant.
Evaluating the Options Now, let's examine the given options and see which one matches the correct formula:
Option 1: E = q d F e (Incorrect, as it involves force and an extra distance term) Option 2: E = d k q (Incorrect, as the distance should be squared) Option 3: E = a 2 ka (Correct, this simplifies to E = a k , which is the electric field at a distance a from a source, but it should be E = a 2 k q )
Option 4: E = d F e (Incorrect, as it involves force but not the charge)
Finding the Closest Match Option 3, E = a 2 ka , can be rewritten as E = a k . However, the correct formula should be E = a 2 k q . If we consider a as the distance d and include the source charge q , the correct formula is E = d 2 k q . Among the given options, E = a 2 ka is closest to the correct form if we assume q = 1 and a is the distance. However, it is not the general formula. There seems to be a typo in the options. The closest correct option is E = a 2 ka if we consider a as the distance and assume q = 1 . However, the general formula is E = d 2 k q .
Conclusion The closest answer to the correct formula E = d 2 k q is E = a 2 ka , which simplifies to E = a k . This is the electric field at a distance a from a source, assuming the source charge q = 1 .
Examples
Understanding the electric field strength is crucial in many real-world applications, such as designing electronic devices, understanding atmospheric phenomena like lightning, and developing medical equipment like MRI machines. For example, when designing a capacitor, engineers need to know the electric field strength between the plates to determine the amount of charge it can store. Similarly, in telecommunications, understanding electric fields helps in optimizing antenna designs for efficient signal transmission.
