A sonometer wire gives frequency \( f_1 \) with tension \( T_1 \). If the tension is made 4 times greater, what is the new frequency? The frequency of a vibrating wire is related to the tension in the wire by the equation: \[ f \propto \sqrt{T} \] where:\( f \) is the frequency,\( T \) is the tension in the wire.
If the tension is increased by a factor of 4, how does the frequency change?
A magnetic field is produced along the axis of a current-carrying loop. The direction and magnitude of the magnetic field at the center of the loop can be determined using the Biot-Savart law. What will be the direction of the magnetic field along the axis of the current loop? The magnetic field produced along the axis of a circular current loop is given by the equation: \[ B = \frac{{\mu_0 I R^2}}{{2 (R^2 + x^2)^{3/2}}} \]where:\( B \) is the magnetic field,\( \mu_0 \) is the permeability of free space,\( I \) is the current,\( R \) is the radius of the loop,\( x \) is the distance from the center of the loop along the axis.