SATHEE: electrostatic-potential-and-capacitance Question 11

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 11

Question: Q. 4. $A$ test charge $q$ is moved without acceleration from $A$ to $C$ along the path from $A$ to $B$ and then from $B$ to $C$ in electric field $E$ as shown in the figure.

(i) Calculate the potential difference between $A$ and C.

(ii) At which point (of the two) is the electric potential more and why?

A [O.D. I, II, III 2012]

Show Answer

Solution:

Ans. Since,

$E = - d V / d r$

$E = (V_{C} - V_{A}) / 4$

$1 / 2$

Therefore, $V_{A} - V_{C} = - 4 E$

At point $C$ , potential is more

$1 / 2$

etric field is in the direction in which the potential decreases.

[CBSE Marking Scheme 2012]

Detailed Answer :

(i) From the figure, as work done is independent of path, so moving a charge $q$ from point $A$ to $B$ and further from point $B$ to $C$ , we will take a direct path from point $A$ to $C$ . So potential difference between points $A$ and $C$ is given as :

$\begin{aligned} V_{C} - V_{A} & = - E . d l & = - \int_{A}^{C} E d l \cos θ \end{aligned}$

As direction of test charge ’ $q$ ’ is opposite to direction of electric field $E$ along $A C$ , so angle between $\vec{E}$ and $\vec{d l}$ will be $180^{\circ}$ , hence we can write this as :

$\begin{aligned} V_{C} - V_{A} & = - E . d l & = - \int_{A}^{C} E d l \cos θ \end{aligned}$

(ii) As direction of electric field is high to low potential, so $V_{C} > V$

Also, $V_{C} - V_{A} = 4 E$ with $E$ as positive $1 / 2$ Potentialincreases when charge is moved against the direction of electric field, so potential will be more at point $C$ .

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 11

Detailed Answer :

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Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 11

Detailed Answer :

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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