Answer
409.8k+ views
Hint: Applying electrified formulas use the given thing , applying integration for both sides there we easily get ${V_1} - {V_2}$ value by putting the values of A and B. In the electrodynamic chapter we have seen questions like this. In this question we ask the potential difference its unit is V.
Formula used:
$dV = - \vec E.d\vec r$
Complete Step by step solution:
$dV = - \vec E.d\vec r$
First we have to write given values
$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}\to
{\vec E} = \left( {Ax + B} \right)\hat i$
Constant values are A=20 SI unit and B=10 SI unit. If the potential at x=1 is ${V_2}$ and that at x=−5 is ${V_2}$ , then ${V_1} - {V_2}$ is
$\eqalign{
& \int\limits_{{v_2}}^{{v_1}} {dV = \int\limits_{ - 5}^1 { - \left( {Ax + B} \right)dx} } \cr
& {v_1} - {v_2} = {\left( { - A\dfrac{{{x^2}}}{2} - Bx} \right)^1}_{ - 5} \cr} $
By simplification we get
$\eqalign{
& \Rightarrow {v_1} - {v_2} = \left( { - \dfrac{A}{2} - B} \right) + \left( {\dfrac{A}{2}25 + B( - 5)} \right) \cr
& \Rightarrow {v_1} - {v_2} = 12A - 6B \cr
& \Rightarrow {v_1} - {v_2} = 240 - 60 \cr
& \therefore {v_1} - {v_2} = 180V \cr} $
Hence, the correct option C.
Additional information:
The negative sign of $dV = - \vec E.d\vec r$this formula shows the direction of E, it is in the direction in which V decreases.
In other words we can say electric field points in the opposite direction to the voltage drop. And it is quite obvious because as you are going in the direction of the electric field you are in a way moving towards negative charges so electric potential is bound to decrease.
We have to practice the derivation of this formula. Then we get a strong hold on to use this formula.
Here we dr is the component of dr in the direction $\hat i$ dr can be either positive or negative depending on which way the external force is displaced. Once this expression becomes an integral then the sign of dr is determined by the limits of integration as we can see here.
Note:
If intensity of electric field is non uniform with respect to distance 'r' , over a given space, we have to use this formula for small segments in which considering uniformity of electric field intensity in that segment. And here we have to remember the negative sign of this formula.
Formula used:
$dV = - \vec E.d\vec r$
Complete Step by step solution:
$dV = - \vec E.d\vec r$
First we have to write given values
$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}\to
{\vec E} = \left( {Ax + B} \right)\hat i$
Constant values are A=20 SI unit and B=10 SI unit. If the potential at x=1 is ${V_2}$ and that at x=−5 is ${V_2}$ , then ${V_1} - {V_2}$ is
$\eqalign{
& \int\limits_{{v_2}}^{{v_1}} {dV = \int\limits_{ - 5}^1 { - \left( {Ax + B} \right)dx} } \cr
& {v_1} - {v_2} = {\left( { - A\dfrac{{{x^2}}}{2} - Bx} \right)^1}_{ - 5} \cr} $
By simplification we get
$\eqalign{
& \Rightarrow {v_1} - {v_2} = \left( { - \dfrac{A}{2} - B} \right) + \left( {\dfrac{A}{2}25 + B( - 5)} \right) \cr
& \Rightarrow {v_1} - {v_2} = 12A - 6B \cr
& \Rightarrow {v_1} - {v_2} = 240 - 60 \cr
& \therefore {v_1} - {v_2} = 180V \cr} $
Hence, the correct option C.
Additional information:
The negative sign of $dV = - \vec E.d\vec r$this formula shows the direction of E, it is in the direction in which V decreases.
In other words we can say electric field points in the opposite direction to the voltage drop. And it is quite obvious because as you are going in the direction of the electric field you are in a way moving towards negative charges so electric potential is bound to decrease.
We have to practice the derivation of this formula. Then we get a strong hold on to use this formula.
Here we dr is the component of dr in the direction $\hat i$ dr can be either positive or negative depending on which way the external force is displaced. Once this expression becomes an integral then the sign of dr is determined by the limits of integration as we can see here.
Note:
If intensity of electric field is non uniform with respect to distance 'r' , over a given space, we have to use this formula for small segments in which considering uniformity of electric field intensity in that segment. And here we have to remember the negative sign of this formula.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)