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An electric dipole in a uniform electric...

An electric dipole in a uniform electric field experiences (When it is placed at an angle `theta` with the field)

A

Both a torque and a net force

B

Only a force but no torque

C

Only a torque but no net force

D

No torque and no net force

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of what happens to an electric dipole placed at an angle θ in a uniform electric field, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Electric Dipole**: An electric dipole consists of two equal and opposite charges, +Q and -Q, separated by a distance 'd'. The dipole moment (p) is defined as \( p = Q \cdot d \). 2. **Visualizing the Electric Field**: Draw a uniform electric field represented by parallel lines. The direction of the electric field (E) is usually indicated from positive to negative. 3. **Placing the Dipole in the Field**: Position the dipole in the electric field such that it makes an angle θ with the direction of the electric field. 4. **Calculating Forces on the Charges**: - The positive charge (+Q) experiences a force \( F_+ = Q \cdot E \) in the direction of the electric field. - The negative charge (-Q) experiences a force \( F_- = -Q \cdot E \) in the opposite direction of the electric field. 5. **Finding the Net Force**: The net force acting on the dipole is the vector sum of the forces on the two charges: \[ F_{\text{net}} = F_+ + F_- = Q \cdot E - Q \cdot E = 0 \] Thus, the net force acting on the dipole is zero. 6. **Calculating the Torque**: The torque (τ) experienced by the dipole in the electric field can be calculated using the formula: \[ \tau = p \cdot E \cdot \sin(\theta) \] where \( p \) is the dipole moment and \( E \) is the electric field strength. Since the dipole is not aligned with the field, it experiences a torque that tends to align it with the field. 7. **Conclusion**: Since the net force on the dipole is zero and there is a non-zero torque acting on it, we conclude that the dipole experiences only a torque and no net force when placed at an angle θ in a uniform electric field. ### Final Answer: The correct option is **C: only a torque but no net force**.
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