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If magnetic field in space is 1Thati, el...

If magnetic field in space is `1Thati`, electric field is `10 N//Chati`, no gravitational field is present and a charged particle is released from rest from origin, it will

A

not move at all

B

move in circular path

C

move in a helical path

D

move on a straight line

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The correct Answer is:
To solve the problem, we need to analyze the forces acting on a charged particle released from rest in the presence of electric and magnetic fields. ### Step-by-Step Solution: 1. **Identify the Given Information**: - Magnetic field, \( \vec{B} = 1 \, \text{Tesla} \) in the direction of \( \hat{i} \). - Electric field, \( \vec{E} = 10 \, \text{N/C} \) in the direction of \( \hat{i} \). - The particle is released from rest at the origin. 2. **Determine the Forces Acting on the Charged Particle**: - The force due to the electric field on a charge \( Q \) is given by: \[ \vec{F_E} = Q \vec{E} = Q \cdot 10 \, \hat{i} = 10Q \, \hat{i} \] - The magnetic force on a charge moving with velocity \( \vec{V} \) in a magnetic field \( \vec{B} \) is given by: \[ \vec{F_B} = Q (\vec{V} \times \vec{B}) \] - Since the particle is released from rest, its initial velocity \( \vec{V} = 0 \). Therefore, the magnetic force is: \[ \vec{F_B} = Q (0 \times \vec{B}) = 0 \] 3. **Analyze the Motion of the Charged Particle**: - The only force acting on the charged particle is the electric force \( \vec{F_E} = 10Q \, \hat{i} \). - Since there is no magnetic force acting on the particle (as it is at rest), the particle will start to accelerate in the direction of the electric field. 4. **Conclusion**: - The charged particle will move in the direction of the electric field (along \( \hat{i} \)) with an increasing velocity due to the constant electric force acting on it. - Since there is no magnetic force acting on it, it will continue to move in a straight line. ### Final Answer: The charged particle will move in a straight line along the direction of the electric field.

To solve the problem, we need to analyze the forces acting on a charged particle released from rest in the presence of electric and magnetic fields. ### Step-by-Step Solution: 1. **Identify the Given Information**: - Magnetic field, \( \vec{B} = 1 \, \text{Tesla} \) in the direction of \( \hat{i} \). - Electric field, \( \vec{E} = 10 \, \text{N/C} \) in the direction of \( \hat{i} \). - The particle is released from rest at the origin. ...
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