Moving Charges And Magnetism

  • Question 1
    CBSEENPH12037570

    A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

    Solution

    Given,
    Current carried by wire, I = 0.40 A,
    Radius of circular wire, r = 8.0 cm = 8×10-2m
    Number of turns in the coil, n = 100

    Using the formula, we get the magnetic field at the centre of coil as

    B = μ0nI2r = 4π×10-7×100×0.42×8.0×10-2T
                   = 3.1 × 10-4T.
                            

    Question 2
    CBSEENPH12037571

    A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

    Solution

    Given,
    Current carried by conductor, I = 35 A
    Distance, r = 20 cm = 0.2 m

    Using Ampere's circuital law we get, 

     B = μ0I2πr = 4π×10-7×352π×0.20T  = 3.5 × 10-5T.

    Question 3
    CBSEENPH12037572

    A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

    Solution
    Given,
    Current carried by wire, I= 50 A
    Distance from the wire, r = 2.5 m
    Magnetic field at point r,  B = ?

    Using ampere's circuital law
                           B = μ0I2πr = 4π×10-7×502π×2.5= 4 × 10-6T 

    The direction of magnetic field can be found out by applying right hand thumb rule. As the direction of current is from north to south represented by thumb, the direction iof magnetic field is vertically upwards in east direction of wire.
    Question 4
    CBSEENPH12037573

    A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

    Solution

    Given, current, I= 90 A
    distance ,r = 1.5 m
    Thus,
    the magnitude of magnetic field is given by Ampere's circuital law 

                   B = μ0I2πr    = 4π×10-7×902π×1.5   = 1.2 × 10-5 T  

    Applying the right-hand thumb rule, we find that the magnetic field at the observation point is directed towards south.

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