Relation between Electric field and Potential
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| Relation between Electric field and Potential |
If a test charge `q_0` is located at any point in an electric field `\vec E`. Then an electric force `\vec F = q_0 \vec E` applies on the test charge by the electric field. In this condition the test charge `q_0` tries to move along the direction of electric field `\vec E` due to this force. Let the external force `\vec F_{ext.}` is applied on the charge `q_0`, which is equal to the electric force `\vec F_e`, but in the opposite direction.
Thus work done in displacing test charge `q_0` from point A to point B by external force.
`dW = - \vec F.d\vecl`
`dW = - q_0 \vec E.d\vecl`
`W = - q_0 \int_A^B \vec E.d\vec l`
The total work done by the electric field on the charge due to the displacement from A to B.
`W = - \int_A^B \vec F.d\vec l`
`W = - \int_A^B q_0 \vec E.d\vec l`
`\frac{W}{q_0} = - \int_A^B \vec E.d\vec l`
`V_B - V_A = - \int_A^B \vec E.d\vec l` `(\because \frac{W}{q_0} = V_B - V_A)`
If the point A to be at infinity, then `V_A =0`
Then,
`V_B - 0 = - \int_{\infty}^B \vec E.d\vec\l`
`V = - \int_{\infty}^B \vec E.d\vec\l` (If `V_B = V`)
Again work done in displacing test charge from point A to point B by the force.
`W_{AB} = - q_0 \int_A^B \vec E.d\vec l`
`U_{B} - U_{A} = - q_0 \int_A^B \vec E.d\vec l` `(\because W_{AB} = U_B - U_A)`
If point A is located at infinity, then no electrostatic force will act between the test charge and source charge, due to which the potential energy of test charge at infinity will be zero it means `U_A = 0`.
`U_{B} - 0 = - q_0 \int_{\infty}^B \vec E.d\vec l`
`U_{B} = - q_0 \int_{\infty}^B \vec E.d\vec l`
Therefore, in this condition, this work will be equivalent to the potential energy of test charge `q_0` at point B in the electric field.
`W_{B} = - q_0 \int_{\infty}^B \vec E.d\vec l`
Related MCQs.
1. How is electric potential defined?
A) The amount of electric charge at a specific point.
B) The amount of electric potential energy per unit charge.
C) The amount of electric current passing through a circuit.
D) The strength of the magnetic field.
2. What are the units in which electric potential is measured?
A) Amperes (A)
B) Joules (J)
C) Volts (V)
D) Ohms (Ω)
3. What role does electric potential play in understanding electricity and magnetism?
A) It determines the direction of electric field lines.
B) It helps in calculating the resistance in a circuit.
C) It represents the work done in bringing charges together.
D) It assists in analyzing the behavior of charged particles.
4. What can be calculated using electric potential in an electric circuit?
A) The amount of charge stored in a capacitor.
B) The strength of the magnetic field.
C) The potential difference between two points in the circuit.
D) The total resistance in the circuit.
5. The potential difference across a resistor is 12 volts. If a current of 2 amperes flows through it, what is the resistance of the resistor?
A) 6 ohms
B) 24 ohms
C) 14 ohms
D) 8 ohms
6. Electric potential is a scalar quantity because:
A) It has both magnitude and direction
B) It depends on the charge of the object
C) It can be positive or negative
D) It only has magnitude
7. The potential difference between two points in an electric field is 6 volts. If a charge of 2 coulombs moves between these points, what is the change in potential energy?
A) 12 joules
B) 3 joules
C) 0.33 joules
D) 0.17 joules
Answers:
1. B
2. C
3. D
4. C
5. A
6. D
7. A
Related Questions
1. Q: How is electric potential defined?
A: Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It represents the work done in bringing a positive unit charge from infinity to that point.
2. Q: What are the units in which electric potential is measured?
A: Electric potential is measured in volts (V).
3. Q: How does the concept of electric potential aid in determining the behavior of charges within an electric field?
A: Electric potential allows us to determine the direction and magnitude of electric field lines, and it helps in calculating the potential difference between two points in an electric circuit. This understanding aids in predicting the movement and distribution of charges within the field.
4. What is electric potential?
Answer: Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It represents the work done in bringing a positive unit charge from infinity to that point.
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