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Which of the following statements is true about the relation between electric field and potential?
- a)Electric field is in the direction in which the potential decreases steepest.
- b)Magnitude of electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point.
- c)In the region of strong electric field, equipotential surfaces are far apart.
- d)Both the statements (a) and (b) are correct.
Correct answer is option 'D'. Can you explain this answer?
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Which of the following statements is true about the relation between e...
In the region of strong electric fields equipotential surfaces are close together and in the region of weak electric fields, equipotential surfaces are far apart.
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Which of the following statements is true about the relation between e...
Relation between Electric Field and Potential
Electric field and potential are two important concepts in electrostatics. The relation between electric field and potential can be explained as follows:
Electric Field in the Direction of Steepest Potential Decrease
When a positive test charge is placed in an electric field, it experiences a force in the direction of the electric field lines. If the test charge is moved along an equipotential surface, no work is done on the charge as potential remains constant. However, when the test charge is moved perpendicular to the equipotential surface, work is done on the charge as potential changes. Therefore, electric field is in the direction in which the potential decreases steepest.
Magnitude of Electric Field
The magnitude of the electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point. Mathematically, it can be represented as:
E = -dV/ds
where E is the magnitude of the electric field, V is the potential, and s is the distance perpendicular to the equipotential surface.
Equipotential Surfaces in Strong Electric Field
In the region of strong electric field, equipotential surfaces are close together as the potential changes rapidly. Conversely, in the region of weak electric field, equipotential surfaces are far apart as the potential changes slowly.
Conclusion
Both statements (a) and (b) are correct. Electric field is in the direction in which the potential decreases steepest, and the magnitude of the electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point. In the region of strong electric field, equipotential surfaces are close together.
Electric field and potential are two important concepts in electrostatics. The relation between electric field and potential can be explained as follows:
Electric Field in the Direction of Steepest Potential Decrease
When a positive test charge is placed in an electric field, it experiences a force in the direction of the electric field lines. If the test charge is moved along an equipotential surface, no work is done on the charge as potential remains constant. However, when the test charge is moved perpendicular to the equipotential surface, work is done on the charge as potential changes. Therefore, electric field is in the direction in which the potential decreases steepest.
Magnitude of Electric Field
The magnitude of the electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point. Mathematically, it can be represented as:
E = -dV/ds
where E is the magnitude of the electric field, V is the potential, and s is the distance perpendicular to the equipotential surface.
Equipotential Surfaces in Strong Electric Field
In the region of strong electric field, equipotential surfaces are close together as the potential changes rapidly. Conversely, in the region of weak electric field, equipotential surfaces are far apart as the potential changes slowly.
Conclusion
Both statements (a) and (b) are correct. Electric field is in the direction in which the potential decreases steepest, and the magnitude of the electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point. In the region of strong electric field, equipotential surfaces are close together.
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Which of the following statements is true about the relation between electric field and potential?a)Electric field is in the direction in which the potential decreases steepest.b)Magnitude of electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point.c)In the region of strong electric field, equipotential surfaces are far apart.d)Both the statements (a) and (b) are correct.Correct answer is option 'D'. Can you explain this answer?
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