Home
Class 12
PHYSICS
A uniform electric field E exists in a r...

A uniform electric field E exists in a region of space. Refer to the given figure for the location of three points A, B and C.

Find: `(a) V_(B)-V_(A)" " (b) V_(C )-V_(A)`

Text Solution

Verified by Experts

(a) Let a test charge `q_(0)` be moving from A to B.

Work done by electric field in moving charge from A to B is given by:
`W_(el) ^(A to B)=q_(0) E xx AB xx cos theta`
`cos theta=(AC)/(AB)`
`rArr W_(el)^(A to B)=q_(0)E xx AC`
`rArr W_(el)^(A to B)=q_(0)Eb`
According to the definition of potential difference we have:
`V_(B)-V_(A)= -(W_(el)^(A to B))/(q_(0)) rArr V_(B)-V_(A)= -Eb`
(b) `W_(el)^(A to C) =q_(0)E xx AC=q_(0)Eb`
`V_(C )-V_(A)= -(W_(el)^(A to C))/(q_(0)) rArr V_(C )-V_(A)= -Eb`
Note: No work is required to move test charge from B to C because electric force becomes perpendicular to the displacement. Points B and C are at same potential, `V_(B)-V_(C )`=0`.
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    MODERN PUBLICATION|Exercise PRACTICE PROBLEMS 1|10 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    MODERN PUBLICATION|Exercise PRACTICE PROBLEMS 2|21 Videos

  • ELECTROMAGNETIC WAVES

    MODERN PUBLICATION|Exercise CHAPTER PRACTICE TEST|14 Videos

  • MAGNETISM AND MATTER

    MODERN PUBLICATION|Exercise CHAPTER PRACTICE TEST FOR BOARD EXAMINATION|16 Videos

Similar Questions

Explore conceptually related problems

Find V_(A)-V_(B)

A uniform electric field exists in a region of space. Potential at potential O,A,B and C are V_(0)=0 and V_(A)=-1V,V_(B)=-6V and V_(C)=-3V respectively. Alll the cubes shown in fig have side length of 1m. ltbr. (a). Find V_(P)-V_(Q) (b). Find the smallest distance of a point from O where the potential is -2V

Consider an x-y plane and mark the locations A, B and C whose coordinates are given to be (5, 2), (5, 8) and (-5, 8) respectively. A uniform electric field of 200 N/C exists in space directed along the negative x-direction. Calculate (i) V_(B)-V_(A) (ii) V_(C )-V_(A) (iii) V_(B)-V_(C ) .

Find the equivalent resistance of the network shown in the figure between the points A and B if (i) V_(A) gt V_(B) (ii) V_(A) lt V_(B)

In uniform electric field E=10 N//C , find a. V_A-V_B , b. VB-V_C

An electric field vec E=(25hat i+30hat j)NC^(-1) exists in a region of space.If the potential at the origin is taken to be zero then the potential at x=2m y=2m is : (A) -110V (B) -140V (D) -120V -130V

Potential difference between points A and B (i.e. V_(A) - V_(B) ) is -----

A uniform electric field of 30NC^(-1) exists along the X-axis calculate the potential difference V_(B)-V_(A) between the points A (4m,2m) and B(10m,5m).