Embibe Experts Solutions for Exercise 1: ICSE-2018

A circular coil carrying a current $\mathrm{I}$ has radius $R$ and number of turns $N$. If all the three, i.e., the current $\mathrm{I}$, radius $R$, and number of turns $N$ are doubled, then, the magnetic field at its center becomes: 

A moving charged particle $\mathrm{q}$ travelling along the positive X-axis enters a uniform magnetic field $\mathrm{B} .$ When will the force acting on $\mathrm{q}$ be maximum?

 A long horizontal wire P carries a current of $50 A$. It is rigidly fixed. Another wire Q is placed directly above and parallel to P as shown in Figure 1 below. The weight per unit length of the wire Q is $0.025 \mathrm{N} {\mathrm{m}}^{-1}$ and it carries a current of $25 A$. Find the distance r of the wire Q from the wire P so that the wire Q remains at rest.

Calculate force per unit length acting on the wire B due to the current flowing in the wire A. (See figure 2 below):

An electric current I flows through an infinitely long conductor as shown in Figure below. Write an expression and direction for the magnetic field at point P.

An electric current I flows through a circular loop as shown in Figure below. Write an expression and direction for the magnetic field at the centre of the loop at point $\mathrm{P}$.

Write Biot-Savart's law in vector form.

Write an expression for force per unit length between two long current-carrying wires, kept parallel to each other, in a vacuum and hence define an ampere, the SI unit of current.