Figure shows , three spherical and equipotential surfaces (marked $1, 2$ and $3$ in the figure) around a point charge $q$ . If the potential difference $V_{1} - V_{2} = V_{2} - V_{3}$ and $t_{1}$ and $t_{2}$ be the distances between them, then which of the following is true?

t_{1} = t_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t_{1} > t_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t_{1} < t_{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

t_{1} \leq t_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $t_{1} < t_{2}$
The potential in the space around a point charge is given by $V (r) = \frac{q}{4 π ϵ_{0} r}$ Let $a, b, c$ be the radii of $1, 2, 3$ respectively.

Thus, $t_{1} = b - a$ and $t_{2} = c - b$

$V_{1} - V_{2} = \frac{q}{4 π ϵ_{0} a} - \frac{q}{4 π ϵ_{0} b} = \frac{q t_{1}}{4 π ϵ_{0} a b}$

$V_{2} - V_{3} = \frac{q}{4 π ϵ_{0} b} - \frac{q}{4 π ϵ_{0} c} = \frac{q t_{2}}{4 π ϵ_{0} b c}$

But $V_{1} - V_{2} = V_{2} - V_{3}$

$\Rightarrow \frac{V_{1} - V_{2}}{V_{2} - V_{3}} = 1$

$\Rightarrow \frac{t_{1}}{a b} \times \frac{b c}{t_{2}} = 1$

$\Rightarrow \frac{t_{1}}{t_{2}} = \frac{a}{c}$

As $a < c$ , we can conclude that $t_{1} < t_{2}$

Hence, option (c) is the correct answer.

Suggest Corrections

Similar questions

A point moves with uniform acceleration and $v_{1}, v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals of time $t_{1}, t_{2}$ and $t_{3}$ . Which of the following relations is correct?

A spherical shell of radius 10 cm is carrying a charge q. if the electric potential at distances 5 cm, 10 cm and 15 cm from the centre of the spherical shell is $V_{1}, V_{2} a n d V_{3}$ respectively, then

Q. A point moves with uniform acceleration and

v_{1}, v_{2}, v_{3}

denote the average velocities in three successive intervals of time

t_{1}, t_{2}, t_{3}

. Then, the relation

\frac{v_{1} - v_{2}}{v_{2} - v_{3}}

$V_{1}, V_{2} a n d V_{3}$ are the potential differences across the $1 Ω, 2 Ω a n d 3 Ω$ resistors and the flow of current is 5 A in a circuit .
Which of the following shows the correct values of $V_{1}, V_{2} a n d V_{3}$ measured in volts?

Q. Three blocks 1, 2 and 3 are arranged as shown in the figure. The velocities of the blocks

v_{1}, v_{2}

and

v_{3}

are shown in the figure. What is the relationship between

v_{1}, v_{2}

and

v_{3}

Join BYJU'S Learning Program

Figure shows , three spherical and equipotential surfaces (marked 1,2 and 3 in the figure) around a point charge q. If the potential difference V1−V2=V2−V3 and t1 and t2 be the distances between them, then which of the following is true?

Figure shows , three spherical and equipotential surfaces (marked $1, 2$ and $3$ in the figure) around a point charge $q$ . If the potential difference $V_{1} - V_{2} = V_{2} - V_{3}$ and $t_{1}$ and $t_{2}$ be the distances between them, then which of the following is true?