Sheet 06 Force Between Two Parallel Current Carrying Conductors.
A rectangular loop of radius \(25cm\) and \(10cm\) carrying a current of \(15A\) is placed with its longer side parallel to a long straight wire \(2.0cm\) apart carrying a current of \(25A\). What is the net force on loop?
Two wires which connect the battery of an automobile to its starting motor carry a current \(300A\) (for short time). What is the force per unit length between the wires, if they are \(70cm\) long and \(1.5cm\) apart? Is the force is attractive or repulsive.
Ans: \(F=0.84N\) and Repulsive.
A wire AB carrying a steady current of \(12A\) and is lying on the table. Another wire CD carrying a current \(5A\) is vertically above AB at a height of \(1mm\). Find: the mass per unit length of the wire CD so that it remains suspended at the position when left free. Give the direction of the current flowing through CD with respect to that of wire AB. Take: \(g=10ms^{-2}\) .
A long straight conductor PQ carrying a current of \(60A\) is fixed horizontally. Another straight conductor XY is kept parallel to PQ at a distance \(4mm\) in air. Conductor XY is free to move and carries a current \(I\) for which the magnetic repulsion just balances the weight of conductor XY. What is the value of \(I\) Mass per unit length for conductor XY is \(10^{- 2}Kgm^{-1}\).
Ans: \(I=32.67A\).
The wires AB,CD and EF are long and have identical resistances. The separation between the neighboring wires is \(2.0cm\). The wire AE and BF have negligible resistance and the ammeter reads \(18A\). Calculate: magnetic force per unit length of AB and CD.
Ans: \(\frac{F}{L_{AB}}=\left(5.4\times10^{-4}\right)\frac{N}{m}\) and \(\frac{F}{L_{CD}}=0\).
A square loop of side \(20cm\) carrying a current of \(1A\) is kept near an infinite long straight wire carrying a current of \(2A\) in the same plane as shown in figure. Calculate: the magnitude and direction of the net force exerted on the loop due to the current carrying conductor.
Ans: \(F_{net}=\left(5.33\times10^{-7}\right)N\).
A circular coil of \(25\) turns and radius \(6cm\), carrying a current of \(10A\) is suspended in a uniform magnetic field of magnitude \(1.2T\). The field lines runs horizontally in the plane of coil as shown in below figure. Calculate: the force and the torque on the coil due to the magnetic field. In which direction should a balancing torque be applied to prevent the coil from turning?
Ans: \(\tau=3.4N-m\).
A solenoid of length \(0.5m\) and having \(500\) turns of wire carries a current of \(4A\). A thin coil having \(10\) turns or wire and radius \(0.01m\) carries a current of \(0.4A\). Calculate: the torque required to hold the coil in middle of the solenoid with its axis perpendicular to the axis of solenoid.
Ans: \(\tau=\left(6.31\times10^{-6}\right)N-m\).
A \(200\) turns coil kept in a magnetic field \(\vec{B}=0.04Wbm^{-2}\) , carries a current of \(1A\). As shown in below diagram. How much torque acts on the coil?
Ans: \(0.32Nm\).
A \(100\) turns closely wound circular coil of radius \(10cm\) carries a current of \(3.2A\). (i) What s the field at the centre of the coil. (ii) What is the magnetic moment of this arrangement? Now, the coil is placed in a vertically plane and is free to rotate about its horizontal axis which coincides with its diameter. A uniform magnetic field of \(2T\) is in the horizontal direction exists such that initially axis of the coil is in the direction of the external magnetic field. The coil rotates through an angle \(90^{o}\) under the influence of magnetic field? (iii) What are the magnitude of the torques on the coil in the initial and final position? (iv)What is the angular speed acquired by the coil when it has rotated through \(90^{o}\)? The moment inertia of the coil is \(0.1kgm^{2}\)
Ans:(i) \(B_{center}=\left(2\times10^{-3}\right)T\) (ii) \(M=10Am^{2}\) (iii) \(\tau=20Nm\) and (iv) \(\omega=20\frac{rad}{s}\).
A parallelogram shaped coil ABCD of sides \(0.5m\) and \(0.3m\) carries a current of \(2A\). It is placed in magnetic field of \(\vec{B}=50T\) parallel to aA-D. Fnd: (i) Force on the sides of the coil and (ii) Torque on coil.
