A particle having a mas of 10–2 kg carries a charge of 5×10−8C. The particle is given an initial horizontal velocity of 105ms−1 in the presence of electric field E→ and magnetic field B→ . To keep the particle moving in a horizontal direction, it is necessary that1) B→ should be perpendicular to the direction of velocity and E→ should be along the direction of velocity.2) Both B→ and E→ should be along the direction of velocity3) Both B→ and E→ are mutually perpendicular and perpendicular to the direction of velocity4) B→ should be along the direction of velocity and E→ should be perpendicular to the direction of velocity.Which one of the following pairs of statements is possible ?

Magnetic force will be perpendicular to the velocity and electrostatic force will be along the velocity. So, net force will not be zero. Hence, the particle will not move in a straight line.If magnetic field is in the direction of the velocity, magnetic force will be zero. While electric force will accelerate the particle in the direction of the electric field. So, the particle will move in a straight line along the direction of the electric field.If both magnetic and electric fields are in perpendicular to the velocity, then the magnetic force and electrostatic force will be in perpendicular direction to the direction of the velocity. So, their resultant may be zero if these are equal and opposite. So, the particle can move in a straight line.If magnetic field is in the direction of the velocity, the magnetic force will be zero. While electrostatic force will be in the direction of the electric field which is perpendicular to the direction of the velocity. So, the particle will not move in straight line. The path will be parabolic.

A particle having a mas of 10–2 kg carries a charge of 5×10−8C. The particle is given an initial horizontal velocity of 105ms−1 in the presence of electric field E→ and magnetic field B→ . To keep the particle moving in a horizontal direction, it is necessary that1) B→ should be perpendicular to the direction of velocity and E→ should be along the direction of velocity.2) Both B→ and E→ should be along the direction of velocity3) Both B→ and E→ are mutually perpendicular and perpendicular to the direction of velocity4) B→ should be along the direction of velocity and E→ should be perpendicular to the direction of velocity.Which one of the following pairs of statements is possible ?

Magnetic force will be perpendicular to the velocity and electrostatic force will be along the velocity. So, net force will not be zero. Hence, the particle will not move in a straight line.If magnetic field is in the direction of the velocity, magnetic force will be zero. While electric force will accelerate the particle in the direction of the electric field. So, the particle will move in a straight line along the direction of the electric field.If both magnetic and electric fields are in perpendicular to the velocity, then the magnetic force and electrostatic force will be in perpendicular direction to the direction of the velocity. So, their resultant may be zero if these are equal and opposite. So, the particle can move in a straight line.If magnetic field is in the direction of the velocity, the magnetic force will be zero. While electrostatic force will be in the direction of the electric field which is perpendicular to the direction of the velocity. So, the particle will not move in straight line. The path will be parabolic.

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A particle having a mas of 10^–2 kg carries a charge of $5 \times 10^{- 8} C$ . The particle is given an initial horizontal velocity of $10^{5} {ms}^{- 1}$ in the presence of electric field $\vec{E}$ and magnetic field $\vec{B}$ . To keep the particle moving in a horizontal direction, it is necessary that
1) $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity.
2) Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity
3) Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity
4) $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity.
Which one of the following pairs of statements is possible ?

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(2) and (4)

(3) and (4)

(1) and (3)

(2) and (3)

answer is D.

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Detailed Solution

Magnetic force will be perpendicular to the velocity and electrostatic force will be along the velocity. So, net force will not be zero. Hence, the particle will not move in a straight line.
If magnetic field is in the direction of the velocity, magnetic force will be zero. While electric force will accelerate the particle in the direction of the electric field. So, the particle will move in a straight line along the direction of the electric field.
If both magnetic and electric fields are in perpendicular to the velocity, then the magnetic force and electrostatic force will be in perpendicular direction to the direction of the velocity. So, their resultant may be zero if these are equal and opposite. So, the particle can move in a straight line.
If magnetic field is in the direction of the velocity, the magnetic force will be zero. While electrostatic force will be in the direction of the electric field which is perpendicular to the direction of the velocity. So, the particle will not move in straight line. The path will be parabolic.

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