Electric Potential And Potential Energy

Question

At a radial distance of 0.5 m from an isolated point charge of 5 nanocoulomb the potential takes a definite value, so what is it?

RankGuru · Accepted Answer

Electric potential due to a point charge is $V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}$, with $\frac{1}{4\pi\varepsilon_0} = 9	imes10^9\ \mathrm{N\,m^2/C^2}$, a formula stated in NCERT Class 12, Chapter 2 (Electrostatic Potential and Capacitance). Here $q = 5	imes10^{-9}$ C and $r = 0.5$ m. Substituting, $V = 9	imes10^9 	imes \frac{5	imes10^{-9}}{0.5}$. The product $9	imes10^9 	imes 5	imes10^{-9} = 45$, and dividing by $0.5$ gives $V = 90$ V. The value 45 V is wrong because it forgets to divide by $r = 0.5$, effectively using $r = 1$ m. The value 180 V is wrong because it divides by $0.25$, mistakenly squaring the distance as if computing a field. The value 9 V is wrong because it drops the factor of 5 from the charge. As potential is a scalar, no direction enters the result. A sign and magnitude check confirms a positive charge gives positive potential, and nano-coulomb charges at half a metre yielding tens of volts is entirely reasonable.

Electric Potential And Potential Energy

Select the correct option:

🔒 Solution Hidden from View

More electrostatics Practice Questions

Two protons are brought from very far apart to a separation of 1 femtometre inside a fusion reactor ...

Moving a charge of 3 microcoulomb between two points raises its potential energy by changing potenti...

Filling the gap of an air capacitor completely with a material of dielectric constant 4 changes its ...

Connecting two capacitors of 4 microfarad and 12 microfarad one after another in a series arrangemen...

Wiring the same 4 microfarad and 12 microfarad capacitors side by side in a parallel bank across one...

Charging a 10 microfarad capacitor in a camera flash circuit up to a potential of 200 volts stores e...

After disconnecting a charged isolated capacitor from its battery, the plate separation is doubled b...

Sketching the surfaces of constant potential around a single isolated positive point charge on a whi...

Once electrostatic equilibrium is reached inside a solid charged metallic conductor, the electric fi...

Inserting a dielectric slab of relative permittivity 5 between capacitor plates while the plates sta...

A cubical Gaussian surface encloses a net charge of 8.85 nanocoulomb at its centre inside a vacuum, ...

Using a long charged wire in a physics demonstration, the field around an infinite line charge follo...

About This Question

Solution