Matt forgot to put the fabric softener in the wash. As his socks tumbled in the dryer, they became charged. If a small piece of lint with a charge of +1.25 E -19 C is attracted to the socks by a force of 3.0 E -9 N, what is the magnitude of the electric field at this location?
2.Suppose an electric field with a magnitude of 2.8 E 4 N/C at a certain location, points due south. If a charge of -4.0 E -6 C is brought to the location, what is the electrostatic force that acts on this charge?
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To solve both of these questions, we need to use the formula for the electric field and the formula for electrostatic force.
1. Magnitude of Electric Field:
The formula for the electric field is given by:
E = F / q
Where E is the electric field (in N/C), F is the electrostatic force (in N), and q is the charge (in C).
In this case, the force F is given as 3.0 E -9 N (meaning 3.0 × 10^(-9) N) and the charge q is given as +1.25 E -19 C (meaning +1.25 × 10^(-19) C).
Substituting these values into the formula, we get:
E = (3.0 E -9 N) / (+1.25 E -19 C)
Now, let's simplify the calculation by converting the scientific notation to decimal numbers:
E = (3.0 × 10^(-9) N) / (1.25 × 10^(-19) C)
To evaluate this expression, divide 3.0 by 1.25:
E = 2.4 × 10^10 N/C
Therefore, the magnitude of the electric field at this location is 2.4 × 10^10 N/C.
2. Electrostatic Force:
The formula for the electrostatic force is given by:
F = E * q
Where F is the electrostatic force (in N), E is the electric field (in N/C), and q is the charge (in C).
In this case, the electric field E is given as 2.8 E 4 N/C (meaning 2.8 × 10^(4) N/C) and the charge q is given as -4.0 E -6 C (meaning -4.0 × 10^(-6) C).
Substituting these values into the formula, we get:
F = (2.8 × 10^4 N/C) * (-4.0 × 10^(-6) C)
To evaluate this expression, multiply 2.8 by -4.0:
F = -11.2 × 10^(-2) N
Therefore, the electrostatic force that acts on the charge is -11.2 × 10^(-2) N. Note that the negative sign indicates that the force is in the opposite direction of the electric field.