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allsm [11]
3 years ago
8

Two circular coils are concentric and lie in the same plane. The inner coil contains 110 turns of wire, has a radius of 0.014 m,

and carries a current of 9.0 A. The outer coil contains 160 turns and has a radius of 0.022 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero?
Physics
1 answer:
Hatshy [7]3 years ago
6 0

Answer:

The current flowing through the outer coils is  

Explanation:

From the question we are told that

   The number of turn of inner coil is N _i  =  110 \  turns

    The radius of inner coil is  r_i  =  0.014 \ m

     The current flowing through the inner coil is  I_i  =  9.0 \ A

     The number of turn of outer coil is N_o  =  160 \ turns

     The radius of outer  coil is r_o  =  0.022\ m

For net magnetic field at the common center of the two coils to be  zero  the current flowing in the outer coil must be opposite to current flowing inner coil

   The magnetic field due to inner coils  is mathematically represented as

            B_i  =   \frac{N_i \mu I}{2 r_i}

     The magnetic field due to inner coils  is mathematically represented as

            B_o  =  \frac{N_o \mu I_o}{2 r_o}

Now for magnetic field at center to be zero

             B_o  =  B_i

So

         \frac{N_i \mu I_i}{2 r_i} =  \frac{N_o \mu I_o}{2 r_o}

=>      \frac{110 * 9}{2 *  0.014} =  \frac{160 *I_o}{2 0.022}

         I_o  = 9.72 \ A

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What is (Fnet3)x, the x-component of the net force exerted by these two charges on a third charge q3 = 55.0 nC placed between q1
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Complete Question

Part of the question is shown on the first uploaded image

The rest of the question

What is (Fnet3)x, the x-component of the net force exerted by these two charges on a third charge q3 = 55.0 nC placed between q1 and q2 at x3 = -1.220 m ? Your answer may be positive or negative, depending on the direction of the force. Express your answer numerically in newtons to three significant figures.

Answer:

The net force exerted on the third charge is  F_{net}=  3.22*10^{-5} \ J

Explanation:

From the question we are told that

    The third charge is  q_3 =  55 nC =  55 *10^{-9} C

    The position of the third charge is  x = -1.220 \ m

     The first charge is q_1 =  -16 nC  =  -16 *10^{-9} \ C

     The position of the first charge is x_1 =  -1.650m

      The second charge is  q_2 =  32 nC  =  32 *10^{-9} C

      The position of the second charge is  x_2 =   0  \ m  

The distance between the first and the third charge is

      d_{1-3} =  -1.650 -(-1.220)

     d_{1-3} = -0.43 \ m

The force exerted on the third charge by the first is  

     F_{1-3} =  \frac{k  q_1 q_3}{d_{1-3}^2}

Where k is the coulomb's constant with a value  9*10^{9} \ kg\cdot m^3\cdot s^{-4}\cdot A^2.

substituting values

      F_{1-3} =  \frac{9*10^{9}* 16 *10^{-9} * (55*10^{-9})}{(-0.43)^2}

       F_{1-3} = 4.28 *10^{-5} \ N

 The distance between the second and the third charge is      

  d_{2-3} =  0- (-1.22)

   d_{2-3} =1.220 \ m

The force exerted on the third charge by the first is mathematically evaluated as

       F_{2-3} =  \frac{k  q_2 q_3}{d_{2-3}^2}

substituting values

       F_{2-3} =  \frac{9*10^{9} * (32*10^{-9}) *(55*10^{-9})}{(1.220)^2}

       F_{2-3} =  1.06*10^{-5} N

The net force is

      F_{net} =  F_{1-3} -F_{2-3}

substituting values

    F_{net} = 4.28 *10^{-5} - 1.06*10^{-5}

    F_{net}=  3.22*10^{-5} \ J

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