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The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m?
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The potential of electric field produced by the point charge at any po...
Understanding Electric Potential and Field
The electric potential V produced by a point charge is vital in determining the electric field intensity. In this case, V = 3x^2 + 5 indicates a relationship where the potential depends on the x-coordinate.
Electric Field Intensity Calculation
To find the electric field intensity (E) from the potential (V), we use the relationship:
- E = -∇V
This means that the electric field is the negative gradient of the electric potential.
Finding the Gradient
For V = 3x^2 + 5:
- The partial derivative with respect to x is:
- dV/dx = 6x
- The partial derivative with respect to y is:
- dV/dy = 0 (since V does not depend on y)
- The partial derivative with respect to z is:
- dV/dz = 0 (since V does not depend on z)
Thus, the gradient (∇V) can be expressed as:
- ∇V = (dV/dx, dV/dy, dV/dz) = (6x, 0, 0)
Evaluating at the Point (-2, 1, 0)
Substituting x = -2 into the gradient:
- ∇V = (6 * -2, 0, 0) = (-12, 0, 0)
Calculating the Electric Field
Now, applying the negative sign to find the electric field:
- E = -∇V = (12, 0, 0)
Thus, at the point (-2, 1, 0), the electric field intensity is:
- E = 12 V/m in the positive x-direction.
Conclusion
The intensity of the electric field at the specified point is indeed -12 V/m, which indicates it is directed towards the negative x-axis. This analysis illustrates how electric potential relates to the electric field and its directional components.
The electric potential V produced by a point charge is vital in determining the electric field intensity. In this case, V = 3x^2 + 5 indicates a relationship where the potential depends on the x-coordinate.
Electric Field Intensity Calculation
To find the electric field intensity (E) from the potential (V), we use the relationship:
- E = -∇V
This means that the electric field is the negative gradient of the electric potential.
Finding the Gradient
For V = 3x^2 + 5:
- The partial derivative with respect to x is:
- dV/dx = 6x
- The partial derivative with respect to y is:
- dV/dy = 0 (since V does not depend on y)
- The partial derivative with respect to z is:
- dV/dz = 0 (since V does not depend on z)
Thus, the gradient (∇V) can be expressed as:
- ∇V = (dV/dx, dV/dy, dV/dz) = (6x, 0, 0)
Evaluating at the Point (-2, 1, 0)
Substituting x = -2 into the gradient:
- ∇V = (6 * -2, 0, 0) = (-12, 0, 0)
Calculating the Electric Field
Now, applying the negative sign to find the electric field:
- E = -∇V = (12, 0, 0)
Thus, at the point (-2, 1, 0), the electric field intensity is:
- E = 12 V/m in the positive x-direction.
Conclusion
The intensity of the electric field at the specified point is indeed -12 V/m, which indicates it is directed towards the negative x-axis. This analysis illustrates how electric potential relates to the electric field and its directional components.
Community Answer
The potential of electric field produced by the point charge at any po...
I am getting +12
by E=-dV/dx
=-6x(at x=-2)=+!2V
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The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m?
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The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m?.
The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential of electric field produced by the point charge at any point (x,y,z) is given by V =3x^2 5,where x,y are in metre and v is in volt.the intensity of electric field at (-2,1,0) is ANS is -12 V/m?.
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