Magnetism And Matter

At the magnetic poles, the magnetic field is vertical. Hence horizontal component is zero and angle of dip is 90^.

Current flows only if there is a potential difference. If no current flows, both bodies must be at the same potential.

Step 1: Self-inductance of a solenoid: L=₀(N²A)/(l)
Step 2: Given N₁:N₂=1:2 and l₁:l₂=1:2.
Step 3: (L₁)/(L₂)=((1)²/1)/((2)²/2)=(1)/(2) L₂:L₁=2:1

Step 1: Definition of torque on magnetic dipole. Torque tends to align the dipole with the magnetic field.
Step 2: Vector form. The torque is given by the cross product of magnetic moment and magnetic field: τ = M × B

Step 1: Torque formula.
The torque on a magnetic moment in a magnetic field is given by the cross product: This represents the force that causes rotational motion.
Thus, the correct answer is (2).

Step 1: Work done in rotating a magnetic moment.
The work done to rotate a magnetic moment through an angle in a magnetic field is given by: where .

Step 2: Calculate the work done.
When , the work done is . Thus, the correct answer is (2).

Magnetic susceptibility of a diamagnetic substance has negative value and is independent of temperature i.e. it remains constant even if the temperature varies.

Step 1: tan δ = (BV)/(BH)
Step 2: BV = BH ⟹ tanδ = 1
Step 3: δ = 45^∘

Step 1: Understand the Motion.
When a charged particle moves perpendicular to a magnetic field, it experiences a centripetal force due to the Lorentz force: $ q v B m r q q q = \frac{mv}{Br} q = \frac{mvB}{r} q = \frac{mB}{vr} q = \frac{Bvr}{m} $