The electric field strength at a particular distance from an electric charge is 2.0 N/C. What is the electric field strength if you are 2 times closer to the same charge?
E is proportional to 1/d^2
so two times closer is four times stronger
E = k Q/d^2
To find the electric field strength if you are 2 times closer to the same charge, you can use the inverse square law for electric fields.
The inverse square law states that the electric field strength is inversely proportional to the square of the distance from the charge. Mathematically, it can be expressed as:
E ∝ 1/d^2
Where E is the electric field strength and d is the distance from the charge.
Now, if the electric field strength at a particular distance is 2.0 N/C, let's assume that this distance is represented by d1. We can write:
E1 = 2.0 N/C
d1 = distance from the charge
If you are 2 times closer to the same charge, the new distance (d2) will be half of the original distance(d1). Mathematically, it can be represented as:
d2 = d1/2
To find the new electric field strength (E2), we can substitute the values into the inverse square law equation:
E1/E2 = (d2/d1)^2
Since we know E1, d2, and d1, we can rearrange the equation to solve for E2:
E2 = E1 * (d1/d2)^2
Substituting the given values:
E2 = 2.0 N/C * (d1/(d1/2))^2
E2 = 2.0 N/C * (2)^2
E2 = 2.0 N/C * 4
E2 = 8.0 N/C
Therefore, if you are 2 times closer to the same charge, the electric field strength will be 8.0 N/C.
To find the electric field strength at a distance, we can use Coulomb's Law, which states that the electric field strength (E) is directly proportional to the magnitude of the electric charge (q) and inversely proportional to the square of the distance (r) between the charge and the point at which the field is being measured.
Mathematically, Coulomb's Law is expressed as:
E ∝ q / r²
Now, let's solve the problem step by step:
1. Assume the initial distance from the electric charge is represented by r₁, and the electric field strength at this distance is E₁ = 2.0 N/C.
2. Given that we are 2 times closer to the same charge, the new distance (r₂) is half of the initial distance, which means r₂ = r₁ / 2.
3. Since E ∝ 1 / r², we can write the following relationship between the initial and new electric field strengths:
E₂ / E₁ = (r₁ / r₂)²
4. Plug in the given values:
E₂ / 2.0 N/C = (r₁ / (r₁ / 2))²
5. Simplify the equation:
E₂ / 2.0 N/C = 2²
E₂ / 2.0 N/C = 4
6. Multiply both sides of the equation by 2.0 N/C:
E₂ = 4 * 2.0 N/C = 8.0 N/C
Therefore, the electric field strength at a distance 2 times closer to the same charge is 8.0 N/C.