149k views
2 votes
Red blood cells can be modeled as spheres of 6.03 um diameter with -2.55 x 10⁻¹² C excess charge uniformly distributed over the surface. Find the electric field at the following locations, with radially outward defined as the positive direction and radially inward defined as the negative direction. The permittivity of free space en is 8.85 x 10⁻¹² C/(V.m).

What is the electric field È inside the cell at a distance of 2.05 um from the center?
Ē₁ = ______ V/m
What is the electric field È, just inside the surface of the cell?
Ē₂= ______ V/m
What is the electric field És just outside the surface of the cell?
Ē₃ = ______ V/m .
What is the electric field És at a point outside the cell 2.05 um from the surface?

User Jlconlin
by
7.8k points

1 Answer

4 votes

Final answer:

The electric field inside a charged spherical object like a red blood cell is zero. The electric field just outside the surface is calculated using Coulomb's Law, taking into consideration the charge and the radius of the sphere. For points farther away, the distance from the center is used in the same calculation.

Step-by-step explanation:

To calculate the electric field at various points around a charged spherical object, we apply the principles of electrostatics, utilizing Gauss's law. Specifically, for a sphere with charge distributed uniformly over its surface, the electric field inside the sphere is zero. Outside the sphere, at a distance r from the center, the electric field is given by E = kq/r², where k is Coulomb's constant (k = 1/(4πε_0), and ε_0 is the permittivity of free space).

Considering a red blood cell modeled as a sphere of diameter 6.03 μm and an excess surface charge of -2.55 x 10⁻¹² C, the electric field È inside the cell at a distance of 2.05 μm from the center (which is less than the radius of the cell) is zero, because the charges are on the surface:

È₁ = 0 V/m

Just inside the surface of the cell, the electric field is also zero for the same reason:

È₂ = 0 V/m

Just outside the surface of the cell, we calculate the electric field using the formula E = kq/r². The radius r here is half the diameter, which is 3.015 μm (or 3.015 x 10⁻¶ m). Using ε_0 = 8.85 x 10⁻¹² C/(V·m), we find that k = 1/(4πε_0) and calculate È₃.

È₃ = (1/(4π x 8.85 x 10⁻¹²)) * (-2.55 x 10⁻¹²) / (3.015 x 10⁻¶)² V/m

To find the electric field at a point 2.05 μm from the surface of the cell, we add this distance to the radius to obtain the total distance from the center of the cell, and then we use the same formula as before to calculate the electric field.

The calculations above are examples but they need the actual values to be plugged in and computed to get the final numeric answers.

User Martin Seeler
by
7.2k points