What is the electric field strength 53 pm from a proton? - Leaving Cert Physics - Question (i) - 2017

To find the electric field strength (E) at a distance from a point charge, we use the formula:

$E = \frac{F}{q}$

where:

• ( F ) is the force experienced by a charge in the electric field,
• ( q ) is the charge experiencing the force.

Alternatively, using Coulomb's Law, the electric field created by a point charge is given by:

$E = \frac{Q}{4\pi \epsilon_0 r^2}$

where:

• ( Q ) is the point charge (for a proton, ( Q = e = 1.6 \times 10^{-19} ) C),
• ( r ) is the distance from the charge (given as 53 pm = ( 53 \times 10^{-12} ) m),
• ( \epsilon_0 ) is the permittivity of free space (approximately ( 8.85 \times 10^{-12} ) C²/(N m²)).

Substituting the values:

1. Convert the distance from pm to meters: ( r = 53 \times 10^{-12} ) m

2. Substitute the values into the equation:

$E = \frac{(1.6 \times 10^{-19})}{4\pi (8.85 \times 10^{-12}) (53 \times 10^{-12})^2}$

3. Perform the calculation to obtain the electric field strength: ( E \approx 5.1 \times 10^{11} ) N C⁻¹ (or equivalently V m⁻¹).