A charged particle moving with a uniform velocity v → , enters a region where uniform electric and magnetic fields E → and B → are present. It passes through the region without any change in velocity. What can we conclude about the ( a ) Relative directions of E → , v → and B → . b Magnitudes of E → and B → .

a Let E → be the strength of electric field and B → be the strength of magnetic field. If F m → and F e → are the electric and magnetic forces acting on the charged particle then, net force F n e t → on that charged particle is given by, From Lorentz force, F n e t → = F e → + F m → F n e t → = q ( E → + v → × B → ) Since, the particle is moving without any change in its velocity, acceleration in the particle, a → = F n e t → m = 0 ⇒ F n e t → = 0 The forces on charged particle due to electric field and magnetic field are equal and opposite. ⇒ 0 = q ( E → + v → × B → ) ⇒ E → = - v → × B → ∴ E → ⊥ v → , E → ⊥ B → and v → is not parallel or anti-parallel to B → . If the charged particle is moving perpendicular to the direction of B → , it experiences a maximum force which acts perpendicular to the direction of B → as well as v → and that force is balanced by electric force which is acting opposite to the direction of B → as well as v → and hence the charged particle moves without any change in velocity. Therefore, All three E → , v → and B → are mutually perpendicular to each other. b The force on charged particle q due to perpendicular magnetic field, F m = q v B sin θ where θ is the angle between the velocity vector and magnetic field. F m = q v B sin 90 ° = q v B Force on charged particle due to perpendicular electric field, F e = q E As the charged particle goes undeflected, so q v B = q E or v = E B

E M B I B E

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 8 - Electromagnetism>EXERCISE 8>Q 48

HARD

12th West Bengal Board

IMPORTANT

Earn 100

Consider the circuit shown in Fig. $8.104$ where $A P B$ and $A Q B$ are semicircles. What is the magnetic field at the centre $c$ of the circular loop?

Important Questions on Electromagnetism

EASY

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 8 - Electromagnetism>EXERCISE 8>Q 49

What is the nature of magnetic field in a moving coil galvanometer ?

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 8 - Electromagnetism>EXERCISE 8>Q 50

A loop of irregular shape, carrying current is placed in an external magnetic field. What shall happen if the wire is flexible?

EASY

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 8 - Electromagnetism>EXERCISE 8>Q 51

An electron beam projected along X-axis experience a force due to a magnetic field along Y-axis. What is the direction of magnetic field?

EASY

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 8 - Electromagnetism>EXERCISE 8>Q 52

Two identical charged particles moving with same speed enter a region of uniform magnetic field. If one of these enters normal to the field direction and the other enters along a direction at