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P 27

Fundamentals Of Physics
Found in: Page 836

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Short Answer

Question: In Fig 29-55, two long straight wires (shown in cross section) carry currents i1=30.0 mA and i1=40.0 mA directly out of the page. They are equal distances from the origin, where they set up a magnetic field. To what value must current i1 be changed in order to rotate 20.0° clockwise?

The value of current i1 is i1 = 61.3mA.

See the step by step solution

Step by Step Solution

Step 1: Given

i) Currents flowing through the two long straight wires are i1 = 30.0mA and i2 = 40.0mA

ii) The rotation of net magnetic field B is θ=20.0° .

Step 2: Determine the formula for the magnetic field as:

Use the concept of the magnetic force due to current in straight wires and trigonometry.




Step 3: Calculate the value to which current i1 must be changed in order to rotate 20.0° clockwise

The value of current i1:

The magnetic field due to a current in straight wire is


The distances of the B1 and B2 are the same; hence they are directly proportional localid="1663143974221" i1 and i2 respectively.

B1 α i1 and

B2 α i2

According to the right hand rule, is going to the y axis and is going along x axis.

The angle of the net field is




Substitute the values and solve as:

θ=tan-140.0 mA30.0 mA


In the problem, the net field rotation is


θ' =53.13°-20.0°

θ' =33.13°

The final value of the current is:



Substitute the values and solve as:

i1=40.0 mAtan33.13°

i1=61.3 mA

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