A wire of radius \(0.7cm\) carrying a current of \(100A\), which is distributed uniformly over its cross-section. Find: the magnetic field; (a) At, \(0.2cm\) away from the axis of the wire. (b) At, the surface of the wire. (c) At, a point outside the wire \(0.3cm\) from the surface of the wire.
Ans:(a) \(B_{inside}=\left(8.16\times10^{-4}\right)T\), (b) \(B_{surface}=\left(2.85\times10^{-3}\right)T\) and (c) \(B_{surface}=\left(2\times10^{3}\right)T\).
A straight thick long wire of uniform cross-section of radius \(a\) is carrying a steady current I. Calculate: the ratio of the magnetic field at a point \(\frac{a}{2}\) above the surface of the wire to that of at a point \(\frac{a}{2}\) below the surface. What is the maximum value of field of the wire?
Ans: \(\frac{B_{P}}{B_{Q}}=\frac{4}{3}\) and \(B_{max}=\frac{\mu_{o}I}{2\pi a}\).
A solenoid of length \(0.5m\) has a radius of \(1cm\) and is made up of \(500\) turns. It carries a current of \(5A\). What is the magnitude of magnetic field inside the solenoid?
Ans: \(B=\left(6.28\times10^{-3}\right)T\).
A toroid has a core of internal radius \(22cm\)around which \(4200\) turns of wire wound. If, the current in the wire is \(10A\), what is the magnetic field; (i) Inside the core of the toroid? (ii) Outside the toroid? (iii) In the empty space surrounded the toroid?
Ans:(i) \(0.04T\) (ii) \(0\) and (iii) \(0\).
A cupper wire having a resistance of \(0.015\Omega\) per meter is used to wind a \(500\) solenoid of radius \(1.5cm\) and length \(25cm\). Find: the e.m.f. of the battery which when connected across the solenoid would produce a magnetic field of \(10^{-2}T\) near the centre of the solenoid.
Ans: \(E=2.8V\).
A long straight solid conductor of radius \(5cm\) carries a current of \(2A\) which is uniformly distributed over its circular cross-section . Find the magnetic field induced at a distance \(4cm\) from the axis of the conductor. Relative permeability of conductor=800.
