What is the value of the charge that experiences a force of [tex]$2.4 \times 10^{-3} N$[/tex] in an electric field of [tex]$6.8 \times 10^{-6} N / C$[/tex]?
Answer (2)
Use the formula F = qE to relate force, charge, and electric field.
Rearrange the formula to solve for the charge: q = E F .
Substitute the given values: q = 6.8 × 1 0 − 6 2.4 × 1 0 − 3 .
Calculate the charge: q ≈ 352.94 C . The closest option is 3.5 × 1 0 1 C .
Explanation
Understanding the Problem We are given the force experienced by a charge in an electric field and the strength of the electric field. We need to find the value of the charge. The formula that relates force, charge, and electric field is F = qE , where F is the force, q is the charge, and E is the electric field.
Rearranging the Formula To find the charge q , we need to rearrange the formula F = qE to solve for q . Dividing both sides of the equation by E , we get: q = E F
Substituting the Values Now, we substitute the given values into the equation. The force F is 2.4 × 1 0 − 3 N , and the electric field E is 6.8 × 1 0 − 6 N / C . Therefore, q = 6.8 × 1 0 − 6 2.4 × 1 0 − 3
Calculating the Charge Calculating the value of q :
q = 6.8 × 1 0 − 6 2.4 × 1 0 − 3 = 352.941176... Rounding to two significant figures, we get q ≈ 350 . Expressing this in scientific notation, we have q ≈ 3.5 × 1 0 2 . However, the options provided are 1.6 × 1 0 − 7 C , 2.5 × 1 0 − 3 C , 2.8 × 1 0 − 3 C , and 3.5 × 1 0 1 C . Since 3.5 × 1 0 2 = 350 and 3.5 × 1 0 1 = 35 , we made an error. Let's recalculate: q = 6.8 × 1 0 − 6 2.4 × 1 0 − 3 ≈ 352.94 Since we need to choose from the given options, and 352.94 is closest to 3.5 × 1 0 2 , let's re-examine the options. The closest option to our calculated value is 3.5 × 1 0 1 C = 35 C . It seems there might be a mistake in the problem statement or the options provided. However, based on our calculation, the closest answer is 3.5 × 1 0 1 C .
Final Answer The value of the charge is approximately 352.94 C . Among the given options, the closest value is 3.5 × 1 0 1 C = 35 C . Therefore, the answer is 3.5 × 1 0 1 C .
Examples
Understanding the relationship between electric force, charge, and electric field is crucial in many real-world applications. For example, in designing electronic devices like capacitors, it's essential to know how much charge can be stored at a certain voltage. Similarly, in particle accelerators, controlling the electric fields allows scientists to manipulate the paths of charged particles. This concept also applies to everyday phenomena like static electricity, where the force between charged objects can be calculated using the same principles.
The charge experiencing a force of 2.4 × 1 0 − 3 N in an electric field of 6.8 × 1 0 − 6 N/C is approximately 352.94 C . Among the options, key or closest option relevant is 3.5 × 1 0 1 C = 35 C if supplied. Please verify the options for accuracy.
;
