Question

1. Calculate the electric field due to a single +1nC point charge at a distance of lm, 2m, and 3m

Answer 1

• Approximately
  `9.0\; \rm N \cdot C^(-1)` at
  `1\; \rm m` from this charge, pointing away from the point charge.
• Approximately
  `2.2\; \rm N \cdot C^(-1)` at
  `\rm 2\; \rm m` from this charge, pointing away from the point charge.
• Approximately
  `1.0\; \rm N \cdot C^(-1)` at
  `3\; \rm m` from this charge, pointing away from the point charge.

Assumption: there is no object between this point charge and the observer.

Step-by-step explanation:

The electric field of a point charge is inversely proportional to the square of the distance from that point charge.

Let
`k` denote Coulomb's constant (
`k \approx 8.98755 * 10^(-9)\; \rm N \cdot m^(2) \cdot C^(-1)`.) Let the magnitude of that point charge be
`q`. At a distance of
`r` from this charge, the electric field due to this charge would be:

`\displaystyle E = (k \cdot q)/(r^(2))`.

Convert the magnitude of the point charge in this question to standard units:

`q = 1\; \rm nC = 10^(-9)\; \rm C`.

Apply that equation to find the magnitude of the electric field due to this point charge:

`r = 1\; \rm m`:

`\begin{aligned} E &= (k \cdot q)/(r^(2)) \\ &= (8.98755 * 10^(-9)\; \rm N \cdot m^(2) \cdot C^(-2) * 10^(-9)\; \rm C)/((1\; \rm m)^(2)) \\ &\approx 9.0\; \rm N \cdot C^(-1)\end{aligned}`.

`r = 2\; \rm m`:

`\begin{aligned} E &= (k \cdot q)/(r^(2)) \\ &= (8.98755 * 10^(-9)\; \rm N \cdot m^(2) \cdot C^(-2) * 10^(-9)\; \rm C)/((2\; \rm m)^(2)) \\ &\approx 2.2\; \rm N \cdot C^(-1)\end{aligned}`.

`r = 3\; \rm m`:

`\begin{aligned} E &= (k \cdot q)/(r^(2)) \\ &= (8.98755 * 10^(-9)\; \rm N \cdot m^(2) \cdot C^(-2) * 10^(-9)\; \rm C)/((3\; \rm m)^(2)) \\ &\approx 1.0\; \rm N \cdot C^(-1)\end{aligned}`.

The direction of the electric field at a point is the same as the direction of a force from this field onto a positive point charge at this point.

Because the
`(+1\; \rm nC)` point charge here is positive, the electric field of this charge would repel other positive point charges. Hence, the electric field around this
`(+1\; \rm nC)\!` point charge at any point in the field would point away from this charge.