NCERT Exemplar Solutions for Class12 Physics – Chapter 4 (Moving Charges & Magnetism) are available here. In this article, you will get solutions to very short answer type questions i.e., from question number 4.12 to 4.16. Solutions of questions from 4.1 to 4.11 are already available in **Part I** & **Part II** of the same article. Solutions of other questions will be available in other parts. These questions are important for various engineering and medical entrance exams like JEE Mains, NEET, WBJEE etc. These questions can also be asked in CBSE Class 12 Physics board exam.

NCERT Exemplar Solutions for CBSE Class 12 Physics, Chapter 4 (from question number 4.12 to 4.16) are given below:

**Very Short Answer Type Question**

**Question 4.12:** Verify that the cyclotron frequency *ω* = *eB*/*m* has the correct dimensions of [T]^{–1}.

**Solution 4.12:**

For a charge particle moving perpendicular to the magnetic field:

(*mv*^{2})/*R* = *qvB*

⇒*qB*/*m* = *v*/*R* = ω

⇒ = ω* *= *qB*/*m* = *v*/*R* = [T]^{–1}.

**CBSE Class 12th Physics Notes: Moving Charges and Magnetism **

**Question 4.13:** Show that a force that does no work must be a velocity dependent force.

**Solution 4.13:**

Let no work is done by a force, so we have

**W** = **F.d l **= 0

As **d l** =

**dt & dt ¹ 0**

*v*Þ **F**.**v** *dt* = 0

Þ **F**.**v **= 0

**F** must be velocity dependent which implies that angle between **F** and **v** is 90°.

If direction of **v** changes then direction of **F** will also change so that above condition is satisfied.

**Question 4.14:** The magnetic force depends on v which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame? Is it reasonable that the net acceleration has a different value in different frames of reference?

**Solution 4.14:**

Magnetic force is frame dependent and it will differ from frame to frame. Net acceleration arising from this is however frame independent (non - relativistic physics) for inertial frames.

**Question 4.15:** Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.

**Solution 4.15:**

Particle will accelerate and decelerate alternatively. So, the radius of path in the Dee’s will remain unchanged.

**Question 4.16:** Two long wires carrying current *I*_{1} and *I*_{2} are arranged as shown in Fig. 4.1. The one carrying current *I*_{1} is along is the x-axis. The other carrying current *I*_{2} is along a line parallel to the y-axis given by *x* = 0 and *z* = *d*. Find the force exerted at O_{2} because of the wire along the *x*-axis.

**Solution 4.16:**

At O_{2}, the magnetic field due to *I*_{1} is along the *y*-axis. The second wire is along the y-axis and hence the force is zero.