Question

The electric field intensity at a point \[P\] due to point charge \[q\] kept at point \[Q\] is \[24N{C^{ - 1}}\] and the electric potential at point is \[12J{C^{ - 1}}\]. The order of magnitude of charge \[q\] is
A. \[{10^{ - 6}}C\]
B. \[{10^{ - 7}}C\]
C. \[{10^{ - 10}}C\]
D. \[{10^{ - 9}}C\]

Answer 1

Hint: The electric charge is assumed to exist at a point, and thus has neither field nor volume. Electric field is defined as the electric force per unit charge. We can find the magnitude of charge by finding the distance between the two given points i.e. point \[P\] and point \[Q\].

Complete step by step answer:
Electric field of point charge
$ E = \dfrac{1}{{4\pi {\varepsilon _o}}}\dfrac{q}{r} $
$ \Rightarrow E = 24N{C^{ - 1}} $
Now electric potential of point charge
$ V = \dfrac{1}{{4\pi {\varepsilon _o}}}\dfrac{q}{r} $
$ \Rightarrow V = 12J{C^{ - 1}} $
The distance between \[p\] and \[q\] is \[r\]. So,
\[ r = \dfrac{V}{{{\text{ }}E}} \]
$ \Rightarrow r = \dfrac{{12}}{{24}} $
$ \Rightarrow r = 0.5m $
Now, we know that
$ q = 4\pi {\varepsilon _o}Vr $
$ \Rightarrow q = \dfrac{1}{{9 \times {{10}^9}}} \times 12 \times 0.5 $
$ \Rightarrow q = 0.667 \times {10^{ - 9}}C $
$\therefore$ The magnitude of the charge is $0.667 \times {10^{ - 9}}C$.
Hence, the correct answer is option (D).

Additional Information:
The Lorentz force moves an electric field E over the charged particle q and a magnetic field B at a speed v. The whole electromagnetic force of a charged particle is called the Lorentz force.
The direction of the electric field is taken in the direction in which it will apply for positive test charge. Electric field moves radially outward from a positive charge and negatively from a negative point charge.

Note: The electrical potential is the amount of a scalar, and the electric field is the amount of a vector. The addition of voltage in the form of a number gives the voltage due to the combination of point charges, while the total electric field is the result of addition to the individual fields as vectors.
The electric potential (voltage) at any point in space generated by a point charge queue is the electric potential energy per unit charge and is the property of the electric effect at that point in space. Since it is a scalar sum, the probability from multiple point charges can only be increased to calculate the probability of the sum of the point charges of the individual charges and the constant charge distribution.