Moving Charges and Magnetism (12Acd05)

Sheet 01 Moving Charges and Magnetic Force & Biot Savart’s Law.

1. Calculate: the force on an electron moving with a velocity of \(6.0\times10^{7}ms^{-1}\) enters a magnetic field of \(1.0T\) at an angle \(30^{o}\).
   
   Ans: \(F_{m}=\left(4.0\times10^{-12}\right)N\).
   
   
2. Copper has \(8.0\times10^{28}\) electrons per cubic metre. A copper wire of length \(1m\) and cross-sectional area \(8.0\times10^{-6}m^{2}\) carrying a current and lying at right angle to the magnetic field of strength \(5\times10^{-3}T\), experiencing a force of \(8.0\times10^{-2}N\). Calculate: the drift velocity of free electrons of the wire?
   
   Ans: \(V_{d}=\left(1.56\times10^{-4}\right)\frac{m}{s}\).
   
   
3. A test charge having \(1.6\times10^{-19}C\) is moving with a velocity \(\vec{v}=\left(2\hat{i}+3\hat{j}\right)ms^{-1}\) in a magnetic field, \(\vec{B}=\left(\hat{i}+3\hat{j}\right)Wb.m^{-2}\). Determine: the magnitude and direction of force acting on test charge.
   
   Ans: \(|F_{m}|=0\) and \(\theta=90^{o}\) .
   
   
4. A proton moves with a velocity \(\vec{v}=\left(2\hat{i}+2\hat{j}-\hat{k}\right) ms^{-1}\) through a region where both electric and magnetic field exists. The electric field, \(\vec{E}=\left(\hat{i}-\hat{j}-3\hat{k}\right)NC^{-1}\) and magnetic field, \(\vec{B}=\left(\hat{i}+2\hat{j}+3\hat{k}\right)Wb.m^{-2}\). Calculate: the Lorentz force acting on the proton.
   
   Ans: \(\vec{F}_{lorentz}=1.6\times10^{-19}\left[9\hat{i}-8\hat{j}-\hat{k}\right]N\).
   
   
5. A proton of kinetic energy \(50MeV\) enters vertically (/at right angle) to the magnetic field of \(2T\) acting horizontally from the south to north. Calculate:
   (i) Magnitude of the magnetic field.
   (ii) Direction of the magnetic force on the proton.
   (iii) Acceleration of the proton.
   Take: mass of the proton as \(1.6\times10^{-27}Kg\).
   
   Ans: (i) \(\left(7.58\times10^{-12}\right)N\) (ii) \(Eastwards\) and (iii) \(a=\left(3.7\times10^{12}\right)\frac{m}{s}\).
   
   
6. A current element \(5\vec{dl}\) is at \(\left(0,0,0\right)\)along X-axis. If, dl is \(10^{-3}m\), Find magnetic field at a distance of \(0.25m\) on Y-axis. Calculate: the strength of the field.
   
   Ans: \(\vec{dB}=\left(8\times10^{-9}\hat{k}\right)T\).
   
   
7. An element \(\vec{dl}=dx\hat{i}\) is placed at the origin and carries a large current, \(I=10A\). What is the magnetic field on Y-axis at a distance of \(0.5m\). Given: \(dx=1cm\)
   
   Ans: \(|\vec{dB}|=\left(4\times10^{-8}\right)T\).
   
   
8. A current element \(5\vec{dl}\) is at \(\left(0,0,0\right)\) along Y-axis. If, \(dl=1cm\), find: the magnetic field at a distance \(20cm\) on the X-axis.
   
   Ans: \(\vec{dB}=\left(12.5\times10^{-8}\right)(-\hat{k})T\).
   
   
9. A wire carries a current of \(8A\) from south to north direction. What is the magnetic field due to \(1cm\) piece of wire at a point \(50cm\), \(45^{o}\) east of north?
   
   Ans: \(|\vec{dB}|=\left(2.26\times10^{-8}\right)T\).