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A uniform electric field and a uniform m...

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the same direction then the electron

A

speed will increase

B

will turn towards left of direction of motion

C

will turn towards right of direction of motion

D

speed will decrease

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The correct Answer is:
To solve the problem, we need to analyze the forces acting on the electron when it is projected in the presence of both a uniform electric field and a uniform magnetic field, which are both acting in the same direction. ### Step-by-Step Solution: 1. **Identify the Forces**: - The electric field \( E \) exerts a force on the electron given by \( F_E = qE \), where \( q \) is the charge of the electron (which is negative). - The magnetic field \( B \) exerts a force on the electron given by the Lorentz force equation \( F_B = q(\mathbf{v} \times \mathbf{B}) \), where \( \mathbf{v} \) is the velocity of the electron. 2. **Direction of Forces**: - Since the electric field and magnetic field are in the same direction, the force due to the electric field \( F_E \) will act in the same direction as the electric field. - For the magnetic force, since the electron has a negative charge, the direction of the magnetic force will be opposite to the direction of the velocity. The cross product \( \mathbf{v} \times \mathbf{B} \) will yield a force that acts perpendicular to both \( \mathbf{v} \) and \( \mathbf{B} \). However, since both fields are in the same direction, the angle \( \theta \) between \( \mathbf{v} \) and \( \mathbf{B} \) is 0 degrees, leading to \( F_B = 0 \). 3. **Net Force on the Electron**: - The net force acting on the electron is therefore only due to the electric field: \( F_{net} = F_E + F_B = qE + 0 = qE \). - Since \( q \) is negative (for an electron), this force will act in the opposite direction to the electric field. 4. **Effect on the Electron's Motion**: - The net force acting on the electron will cause it to accelerate in the opposite direction to the electric field. - As a result, the speed of the electron will decrease because the force is acting against its motion. 5. **Conclusion**: - Therefore, the correct answer is that the speed of the electron will decrease. ### Final Answer: The speed of the electron will decrease.

To solve the problem, we need to analyze the forces acting on the electron when it is projected in the presence of both a uniform electric field and a uniform magnetic field, which are both acting in the same direction. ### Step-by-Step Solution: 1. **Identify the Forces**: - The electric field \( E \) exerts a force on the electron given by \( F_E = qE \), where \( q \) is the charge of the electron (which is negative). - The magnetic field \( B \) exerts a force on the electron given by the Lorentz force equation \( F_B = q(\mathbf{v} \times \mathbf{B}) \), where \( \mathbf{v} \) is the velocity of the electron. ...
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NARAYNA-MOVING CHARGES AND MAGNETISM-EXERCISE - 3
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  15. Two identical long conducting wires AOB and Cod are placed at right an...

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  16. A wire carrying current I has the shape as shown in the adjoining ...

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  17. A long wire carries a steady curent . It is bent into a circle of one ...

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  18. An electron is moving in a circular path under the influence of a tran...

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  19. A long staright wire of radius a carries a steady current I. The cure...

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  20. A square loop of ABCD carrying a current i, is placed near and coplana...

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