Question

A uniform electric field and a uniform magnetic field are produced and pointed in the same direction. A proton is projected with its velocity pointing in the same direction:
1. The proton will turn to its left
2. The proton will turn to its right
3. The proton velocity will increase in magnitude
4. The proton velocity will decrease in magnitude

Answer 1

Correct Answer - Option 3 : The proton velocity will increase in magnitude

CONCEPT:

Lorentz force:

• It is defined as the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force on the charged particle is called the Lorentz force and is given by

​⇒ FL = qE + qvBsinθ 

• A charged particle experiences a force when it moves in a magnetic field.
• The magnetic force is given as,

​
⇒ F = qvBsinθ

Electric field intensity: 

• It is defined as the force experienced by a unit positive test charge in the electric field at any point.
• The positive charge experiences a force in the direction of the electric field and the negative charge experiences a force in the direction opposite of the electric field.

\(⇒ E=\frac{F}{q_{o}}\)

Where, F =  force due to magnetic field, m = mass, q = magnitude of charge, v = speed of charge, E = electric field, B = magnetic field and θ = angle between v and B

EXPLANATION:

• Since the direction of the magnetic field and the velocity of the proton is the same so,

⇒ θ = 0°

• Magnetic force on the proton is,

⇒ F_B = qvB × sin0

⇒ F_B = 0     -----(1)

• The force due to electric field on the proton is given as,

​⇒ FE = eE     -----(2)

• The positive charge experiences a force in the direction of the electric field and the negative charge experiences a force in the direction opposite of the electric field.

Where e = charge on a proton

Therefore total force on the proton is given as,

​⇒ FL = eE     -----(3)

• The total force on the proton is in the direction of its motion, therefore we can say that the proton will accelerate without changing the direction.
• So the proton velocity will increase in magnitude. Hence, option 3 is correct.