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CodeVID-P12-02-CH-01
Magnetic Effects of Current and Magnetism — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Take $\mu_0=4\pi\times10^{-7}$ T m/A. Draw neat labelled diagrams wherever asked. For full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
6 × 1 = 6 marks
1.
The Biot-Savart law gives $dB$ proportional to:
- A.$r^2$
- B.$\frac{\sin\theta}{r^2}$
- C.$\frac{1}{\sin\theta}$
- D.$r$
2.
Field inside a long solenoid is:
- A.$\frac{\mu_0 I}{2\pi a}$
- B.$\mu_0 n I$
- C.$\frac{\mu_0 I}{2R}$
- D.zero
3.
The magnetic force on a charge moving parallel to B is:
- A.maximum
- B.zero
- C.half maximum
- D.negative
4.
Two parallel currents in the same direction:
- A.repel
- B.attract
- C.do nothing
- D.rotate
5.
Torque on a current loop is:
- A.$BIL$
- B.$qvB$
- C.$NIAB\sin\theta$
- D.$\mu_0 n I$
6.
At the magnetic equator the angle of dip is:
- A.90 degrees
- B.45 degrees
- C.0 degrees
- D.30 degrees
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
7.
State the Biot-Savart law in vector form.
8.
Why does the magnetic force do no work on a moving charge?
9.
Write the torque and potential energy of a magnetic dipole in a field.
10.
Define declination and angle of dip.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
11.
Derive the field of a long straight wire using Ampere's circuital law.
12.
Compare diamagnetic, paramagnetic and ferromagnetic materials by their susceptibility.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
13.
Describe the principle, construction and working of a cyclotron, and derive the cyclotron frequency $f=\frac{qB}{2\pi m}$.
14.
Draw and explain the hysteresis loop of a ferromagnet. Define retentivity and coercivity and state why soft iron suits cores and steel suits permanent magnets.
Answer Key
Section A — Multiple Choice Questions
- (B) $\frac{\sin\theta}{r^2}$
- (B) $\mu_0 n I$
- (B) zero
- (B) attract
- (C) $NIAB\sin\theta$
- (C) 0 degrees
Section B — Short Answer (2 marks)
- $d\vec{B}=\frac{\mu_0}{4\pi}\frac{I\,d\vec{l}\times\hat{r}}{r^2}$.
- It is perpendicular to the velocity, so $\vec{F}\cdot\vec{v}=0$.
- $\tau=mB\sin\theta$; $U=-mB\cos\theta$.
- Declination: angle between geographic and magnetic north; dip: angle of total field with the horizontal.
Section C — Short Answer (3 marks)
- By symmetry $B(2\pi a)=\mu_0 I$, so $B=\frac{\mu_0 I}{2\pi a}$.
- Dia: $\chi<0$; para: small $\chi>0$ ($\chi\propto1/T$); ferro: large $\chi>0$.
Section D — Long Answer (5 marks)
- Ion accelerated across the dees and bent into semicircles by B; resonance gives $f=\frac{qB}{2\pi m}$, $E_{max}=\frac{q^2B^2R^2}{2m}$.
- B lags H around a closed loop; soft iron has a thin loop (low loss) for cores; steel has a wide loop (high retentivity) for permanent magnets.
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