Question

In: Physics

A charge of q = 4.00 ✕ 10−9 C is spread evenly on a thin metal...

A charge of q = 4.00 ✕ 10−9 C is spread evenly on a thin metal disk of radius 0.160 m. HINT (a) Calculate the charge density (in C/m2) on the disk. C/m2 (b) Find the magnitude of the electric field (in N/C) just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge. N/C

Solutions

Expert Solution

Given data:

Charge on thin metal disk = 4 x 10-9 C

Radius of the disk = 0.160 m

Answer a)

Charge density of the disc will be given by:

Where q is the charge on the disk

r is the radius of the disk

Which is the required answer

Answer b)

Electric field due to a thin circular disk is given by:

Where is the surface charge density

is the absolute permittivity

R is the radius of the disk

x is the distance from the center of the disk where electric field measurement is being made

For electric field just above the center of the disk . Therefore above formula takes the form:

Substituting the values in above formula we get:

Which is the required answer

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