Question

a charged belt, 50 cm wide, travels at 30 m/s between a source of charge and a sphere.the belt carries charge into the sphere at a rate corresponding to 100 ma. compute the surface charge density on the belt

Answer 1

To calculate the surface charge density on the belt, we use the formula σ = I/(v·w) with the provided values, resulting in a surface charge density of 0.00667 C/m^2.

Step-by-step explanation:

The student is asking about the surface charge density on a moving belt that is being used to transfer charge to a sphere.

The belt is given a width and a speed, and the current (which is the rate of charge transfer) is provided.

To find the surface charge density, we need to start with the basic relationship between current (I), charge (Q), and time (t): I = Q/t.

Since the belt moves at a constant speed, the charge transported per meter would be I/v, where v is the linear velocity of the belt.

Given the width of the belt, we can calculate the surface charge density (σ) using the formula σ = I/(v·w), where w is the width of the belt.

Plugging in the provided values, we get:

• Current, I = 100 mA = 100 x 10-3 A
• Velocity, v = 30 m/s
• Width, w = 50 cm = 0.5 m

Therefore, the surface charge density is:

σ = I/(v·w) = (100 x 10-3 A) / (30 m/s · 0.5 m)

= 0.00667 C/m2