Advertisements
Advertisements
Question
Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding these points) is situated while moving from A to B. The potential
Options
continuously increases
continuously decreases
increases then decreases
decreases then increases
Advertisements
Solution
decreases then increases
Let the distance between the points A and B be r.
Let us take a point P at a distance x from A (x < r).
Electric potential V at point P due to two charges of equal magnitude q is given by
\[V = \frac{q}{4\pi \in_0 x} + \frac{q}{4\pi \in_0 (r - x)}\]
\[ \Rightarrow V = \frac{qr}{4\pi \in_0 x(r - x)}\]
Now, differentiating V with respect to x, we get
\[\frac{dV}{dx} = \frac{- qr(r - 2x)}{4\pi \in_0 x^2 (r - x )^2}\]
Therefore, x = r/2.
It can be observed that \[\frac{dV}{dx} < 0\] for x < r/2.
Thus, the potential is decreasing first.
At x = r/2, the potential is minimum.
As
APPEARS IN
RELATED QUESTIONS
Two point charges qA = 3 μC and qB = −3 μC are located 20 cm apart in vacuum.
- What is the electric field at the midpoint O of the line AB joining the two charges?
- If a negative test charge of magnitude 1.5 × 10−9 C is placed at this point, what is the force experienced by the test charge?
An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 N C−1 (Millikan’s oil drop experiment). The density of the oil is 1.26 g cm−3. Estimate the radius of the drop. (g = 9.81 m s−2; e = 1.60 × 10−19 C).
Can two equipotential surfaces cut each other?
If a charge is placed at rest in an electric field, will its path be along a line of force? Discuss the situation when the lines of force are straight and when they are curved.
If 109 electrons move out of a body to another body every second, how much time is approximately required to get a total charge of 1C on the other body?
Electrostatic force is the force exerted by ______.
Assuming the earth to be a sphere of a uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed 250 Non the surface?
An electromagnetic field is defined as a time-dependent combination of electric and magnetic fields. Which characteristic distinguishes it from a static electric field?
The electric field \[\vec{E}\] at a point is defined as the ratio of the electrostatic force \[\vec{F}\] to a vanishingly small positive test charge q₀. What is the SI unit of the electric field?
For static charges at rest, which statement correctly describes the role and characteristics of the electric field?
Electromagnetic waves, such as sunlight or radio signals, transport energy through space from a source to a receiver. What does this phenomenon demonstrate about the nature of electric and magnetic fields?
An electron falls through a distance h = 1.5 cm in a uniform electric field E = 2.0 × 10⁴ N C⁻¹. Using the formula \[t = \sqrt{\frac{2hm}{qE}}\] and the electron mass mₑ = 9.1 × 10⁻³¹ kg with charge q = 1.6 × 10⁻¹⁹ C, what is the approximate time of fall?
The electric field \[\vec{E}\] is defined such that the force on a test charge q₀ is given by \[\vec{F} = q_0\vec{E}\]. What is the conceptual significance of defining the field as force per unit charge rather than simply force itself?
An accelerated charge generates an electromagnetic wave while a stationary charge generates only a static electric field. What fundamental principle explains this difference in behavior?
An electric field has SI units of N C⁻¹. Express the dimensional relationship between force (F), charge (q₀), and the electric field (E).
