A Hall probe is placed near one end of a solenoid that has been wound on a soft-iron core, as shown in Fig. 9.1.

Question 9

(a) A Hall probe is placed near one end of a solenoid that has been wound on a soft-iron core, as shown in Fig. 9.1.

 Fig. 9.1

 

The current in the solenoid is switched on.

The Hall probe is rotated until the reading VH on the voltmeter is maximum.

 

The current in the solenoid is then varied, causing the magnetic flux density to change.

The variation with time t of the magnetic flux density B at the Hall probe is shown in Fig. 9.2.

 

Fig. 9.2

 

At time t = 0, the Hall voltage is V0.

On Fig. 9.3, draw a line to show the variation with time t of the Hall voltage VH for time t = 0 to time t = t4.

Fig. 9.3

[2]

 

 

(b) The Hall probe in (a) is now replaced by a small coil of wire connected to a sensitive voltmeter, as shown in Fig. 9.4.

Fig. 9.4

 

The magnetic flux density, normal to the plane of the small coil, is again varied as shown in Fig. 9.2.

 

On Fig. 9.5, draw a line to show the variation with time t of the e.m.f. E induced in the small coil for time t = 0 to time t = t4.

Fig. 9.5

[3]

 [Total: 5]

 

Reference: Past Exam Paper – November 2018 Paper 42 Q9

 

Solution:

(a)

0 → t1 horizontal straight line at non-zero value of VH

and

t3 → t4 horizontal straight line at different non-zero VH

 

t1 → t3 straight diagonal line with negative gradient

and

graph line starts at (0, V0) and ends at (t4, –2V0)

 

{Hall voltage: V_H = BI / ntq

The Hall voltage is proportional to the magnetic flux density B.

 

From t= 0 to t1, B is constant, so VH is also constant (= V₀).

 

From t1 to t3, B decreases at a constant rate (constant gradient). So, VH also decreases. At t3 the value of B is negative and twice that at t1, so VH will also be negative and twice larger (= - 2V₀).

 

From t3 to t4, B is constant and so, VH is also constant.}

 

 

(b)

E = 0 for 0 → t1 and t3 → t4

E is non-zero at all points between t1 → t3

E has constant magnitude between t1 → t3

 

{In this case, electromagnetic induction occurs.

From Faraday’s law, the induced e.m.f. is proportional to the rate of change of B.

 

From t = 0 to t1, B is not changing, so no e.m.f. is induced.

 

From t1 to t3, B is decreasing at a constant rate (constant gradient). So, the e.m.f. induced is also constant from t1 to t3.

 

From t3 to t4, B in not changing, so no e.m.f. is induced.}