The electrical force, W, experienced by two charged particles, q1 and q2, is giv

Question

The electrical force, W, experienced by two charged particles, q1 and q2, is given in terms of a known constant, k, and the distance of separation, r, as:

W = k*q1*q2/r^2

Assume that the charges and the distance are measured with a 10% uncertainty (e.g. Ur = 0.1*r).

Which of the following would reduce the uncertainty in W the most?

Decreasing the uncertainty in both charge measurements to 5%, while the uncertainty in distance remains at 10%.

Decreasing the uncertainty in the distance measurement to 5%, while the uncertainty in both charge measurements remain at 10%.

Neither. Both options decrease the uncertainty in W equally.

Decreasing the uncertainty in both charge measurements to 5%, while the uncertainty in distance remains at 10%.

Decreasing the uncertainty in the distance measurement to 5%, while the uncertainty in both charge measurements remain at 10%.

Neither. Both options decrease the uncertainty in W equally.

Explanation / Answer

Ans:

Uncertainity in W can be expressed as:

dW/W=dq1/q1+dq2/q2+2dr/r

=0.1+0.1+2*0.1

=0.4

for a) dW/W=0.05+0.05+2*0.1=0.3

b)dW/W=0.1+0.1+2*0.05=0.3

Both options decrease the uncertainty in W equally.

Hence Option C is correct.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.