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Assertion : Two equipotential surfaces cannot cut each other.
Reason : Two equipotential surfaces are parallel to each other.
Two equipotential surfaces are not necessarily parallel to each other.
What is the defining characteristic of an external electric field when considering the potential energy of a charge within it?
According to the NCERT text, 'The external field E is not produced by the given charge(s) whose potential energy we wish to calculate. E is produced by sources external to the given charge(s).' (Section 2.8.1).
The potential energy of a single charge 'q' at a point 'r' in an external electric field is given by:
The NCERT states, 'Potential energy of q at r in an external field = qV(r) where V(r) is the external potential at the point r.' (Eq. 2.27 and accompanying text).
Which of the following statements is true regarding the influence of a charge 'q' on the external sources producing the electric field?
The provided text mentions, 'We assume that the charge q does not significantly affect the sources producing the external field. This is true if q is very small, or the external sources are held fixed by other unspecified forces.' (Section 2.8).
If an electron with charge $q = e = 1.6 \times 10^{-19} C$ is accelerated by a potential difference of 1 Volt, what is the energy gained in Joules?
The NCERT states, 'if an electron with charge $q = e = 1.6 \times 10^{-19} C$ is accelerated by a potential difference of $\Delta V = 1$ volt, it would gain energy of $q\Delta V = 1.6 \times 10^{-19} J$.' (Section 2.8.1).
What is the equivalent energy value of 1 MeV in Joules?
The NCERT specifies energy units: '1 MeV = $10^6 eV = 1.6 \times 10^{-13} J$.' (Section 2.8.1).
For a system of two charges $q_1$ and $q_2$ located at $r_1$ and $r_2$ respectively, in an external field $V(r)$, the total potential energy of the system is given by:
The total potential energy of the system is the sum of the work done in bringing each charge into the external field and the work done against the field of the other charge. The NCERT states, 'Potential energy of the system = the total work done in assembling the configuration $= q_1V(r_1) + q_2V(r_2) + \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r_{12}}$' (Eq. 2.29).
When bringing a charge $q_2$ from infinity to a point $r_2$ in an external field and in the presence of another charge $q_1$ (already at $r_1$), the work done involves contributions from:
The NCERT text explains: 'Next, we consider the work done in bringing $q_2$ to $r_2$. In this step, work is done not only against the external field E but also against the field due to $q_1$.' (Section 2.8.2).
A dipole with charges $+q$ and $-q$ is placed in a uniform electric field $E$. If the dipole moment $\vec{p}$ is perpendicular to $\vec{E}$ (i.e., $\theta = \pi/2$), and the potential energy is chosen to be zero at this angle, what is the potential energy when the dipole makes an angle $\theta$ with the field?
For a dipole in an external field, the potential energy is given by $U(\theta) = -pE \cos\theta$. This formula is derived by integrating the work done from an initial $\theta_0 = \pi/2$ (where $U=0$) to a final $\theta$. The NCERT states, 'We can then write, $U(\theta) = -pE \cos\theta$' (Eq. 2.32).
In a uniform electric field, an electric dipole experiences:
The NCERT states, 'As seen in the last chapter, in a uniform electric field, the dipole experiences no net force; but experiences a torque $\vec{\tau} = \vec{p} \times \vec{E}$.' (Section 2.8.3).
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