Open Question
A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ₀x/L, where x is measured from the rod's left end.a. What is λ₀ in terms of Q and L?
24. Electric Force & Field; Gauss' Law
Electric Charge
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A ring of charge lies in the xy-plane with its center at the origin. The ring has a radius of 87 cm and a total charge of . What is the linear charge density on the ring?
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Verified step by step guidance1
Understand the concept of linear charge density, which is defined as the charge per unit length along a line or curve. It is denoted by the symbol \( \lambda \).
Identify the given values: the total charge \( Q = 130 \mu C \) and the radius of the ring \( r = 87 \text{ cm} \). Convert these values to standard units: \( Q = 130 \times 10^{-6} \text{ C} \) and \( r = 0.87 \text{ m} \).
Calculate the circumference of the ring, which is the total length of the ring. Use the formula for the circumference of a circle: \( C = 2\pi r \).
Determine the linear charge density \( \lambda \) using the formula \( \lambda = \frac{Q}{C} \), where \( Q \) is the total charge and \( C \) is the circumference of the ring.
Substitute the values of \( Q \) and \( C \) into the formula to find \( \lambda \). This will give you the linear charge density in \( \text{C/m} \).
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