A small glass bead that has been charged to 4.4 nC? What is the strength of the electric field 2.0 cm from the center of the bead?
Please show all work
To find the strength of the electric field at a specific distance from a charged object, you can use Coulomb's Law. Coulomb's Law states that the electric field strength (E) at a distance (r) from a point charge (Q) is given by:
E = k * Q / r^2
Where:
E is the electric field strength
k is Coulomb's constant, approximately equal to 8.99 x 10^9 N m^2/C^2
Q is the charge of the object in coulombs (C)
r is the distance from the center of the object in meters (m)
In this case, we have a glass bead with a charge of 4.4 nC, which is equivalent to 4.4 x 10^-9 C. And we want to find the electric field strength at a distance of 2.0 cm, which is equivalent to 0.02 m.
Now, let's calculate:
E = (8.99 x 10^9 N m^2/C^2) * (4.4 x 10^-9 C) / (0.02 m)^2
First, simplify the numerator:
= (8.99 x 4.4) x (10^9 x 10^-9) N m^2 / C^2
Now multiply the numbers:
= 39.556 N m^2 / C^2
Finally, divide by the squared distance:
= 39.556 N m^2 / C^2 / (0.02 m)^2
= 39.556 N m^2 / C^2 / 0.0004 m^2
= 98,890 N/C
Therefore, the strength of the electric field 2.0 cm from the center of the bead is 98,890 N/C.