Torque on a current loop: Solved Example Problems

Expression for torque on a current loop placed in a magnetic field: Solved Example Problems

EXAMPLE 3.28

Consider a circular wire loop of radius R, mass m kept at rest on a rough surface. Let I be the current flowing through the loop and  be the magnetic field acting along horizontal as shown in Figure. Estimate the current I that should be applied so that one edge of the loop is lifted off the surface?

Solution

When the current is passed through the loop, the torque is produced. If the torque acting on the loop is increased then the loop will start to rotate. The loop will start to lift if and only if the magnitude of magnetic torque due to current applied equals to the gravitational torque as shown in Figure

The current estimated using this equation should be applied so that one edge of loop is lifted of the surface.

Moving coil galvanometer: Solved Example Problems

EXAMPLE 3.29

The coil of a moving coil galvanometer has 5 turns and each turn has an effective area of 2 × 10-2 m2. It is suspended in a magnetic field whose strength is 4 × 10-2 Wb m-2. If the torsional constant K of the suspension fibre is 4 × 10-9 N m deg-1.

(a) Find its current sensitivity in degree per micro - ampere.

(b) Calculate the voltage sensitivity of the galvanometer for it to have full scale deflection of 50 divisions for 25 mV.

(c) Compute the resistance of the galvanometer.

Solution

The number of turns of the coil is 5 turns

The area of each coil is 2 × 10-2 m2

Strength of the magnetic field is 4 × 10-2 Wb m-2

Torsional constant is 4 × 10-9 N m deg-1

EXAMPLE 3.30

The resistance of a moving coil galvanometer is made twice its original value in order to increase current sensitivity by 50%. Will the voltage sensitivity change? If so, by how much?.

Solution

Yes, voltage sensitivity will change.

Voltage sensitivity is Vs = Is/R

When the resistance is doubled, then new resistance is R ′ = 2R

Increase in current sensitivity is

Hence the voltage sensitivity decreases. The percentage decrease in voltage sensitivity is