Physics Electrostatics DUHS 2022
PMDC Verified Question 78 of 131
Q.138 In equation \( E = - \frac{\Delta V}{\Delta r} \). Negative sign indicates that:
A
'E' point towards increasing 'V'
B
'E' point towards decreasing 'V'
C
'E' is perpendicular 'V'
D
'E' is parallel to '\( \Delta V \)'
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 'E' point towards decreasing 'V'
1. Concept:

The electric field vector inherently points from regions of positive charge (high potential) toward regions of negative charge (low potential).

2. Formula:

$$ \vec{E} = - \nabla V $$

3. Solution:

  • The potential gradient formula equates the electric field to the spatial rate of change of voltage.


  • The negative sign serves purely as a directional indicator, proving that if you walk strictly in the direction of the Electric field (\( E \)), the voltage (\( V \)) will steadily decrease.


4. Why other options are incorrect:

If E pointed towards increasing V, the equation would be positive. Field lines and equipotential lines are perpendicular, but this equation describes the gradient line itself, not the equipotential surface.

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