The self induced e.m.f created in a coil has the value of 24mV at the instant when the current is 4A and varies at the rate of 10A/s. What is the value of the self magnetic flux kn the coil at this instant?
To determine the value of the self magnetic flux in the coil at the given instant, we can use Faraday's law of electromagnetic induction.
Faraday's law states that the induced electromotive force (emf) in a coil is directly proportional to the rate of change of magnetic flux through the coil. Mathematically, it can be expressed as:
emf = -N * (dΦ/dt)
Where:
emf is the induced electromotive force
N is the number of turns in the coil
(dΦ/dt) is the rate of change of magnetic flux through the coil
In this case, we are given that the emf is 24mV and the rate of change of current is 10A/s. We need to find the value of the self magnetic flux (Φ).
First, we rearrange the equation to solve for (dΦ/dt):
(dΦ/dt) = -emf / N
Plugging in the given values:
(dΦ/dt) = -24mV / N
Now, we can substitute the given current value (4A) into the equation:
(dΦ/dt) = -24mV / (4A)
(dΦ/dt) = -6mV/A
Since the rate of change of current is measured in A/s, we need to multiply the above result by the rate of change of current (10A/s):
(dΦ/dt) = -6mV/A * 10A/s
(dΦ/dt) = -60mV/s
Therefore, the rate of change of magnetic flux through the coil is -60mV/s.
To find the value of the magnetic flux at the given instant, we can integrate the rate of change of magnetic flux with respect to time. However, since the initial magnetic flux value is not provided, we cannot determine the absolute value of the magnetic flux. We can only determine the rate of change of magnetic flux.
Hence, the value of the self-magnetic flux in the coil at this instant is unknown without further information.